Among igneous rocks, i.e. those formed from magma or molten rock, the most important difference may be between plutonic and volcanic rocks. Plutonic rocks are formed underground. They involve the "intrusion" or insertion of magma between other rocks, which then cools below the surface. Volcanic rocks are formed above ground. They involve the "extrusion" or eruption of magma, which then is called "lava." The lava cools upon or very close to the surface. 
Volcanic rocks can also form from "ash", which is simply pulverized rock blown into the air (not like the "ash" that results from burning wood) -- larger rocks are "bombs."
Plutonic rocks are named after Pluto, the Greek god of the underworld, although the word literally means "wealth," probably because precious metals are generally dug out of the ground. Indeed, gold and silver are characteristically found in "veins," which are intrusions and so part of plutonic rocks. Volcanic rocks are named after volcanoes, which erupt the lava; and volcanoes are named after Vulcan, the Roman god of fire and metalworking.
In the history of geology, there used to be rocks named after another Classical god, namely "neptunian" rocks named after Neptune, the Roman god of the sea. Neptunian rocks were those formed under water. Originally, some people thought that all rocks were neptunian. When it was demonstrated that volcanic rocks came from volcanoes, there was at first a struggle over whether rocks like granite were neptunian or volcanic. It turned out that they were neither. Granite is plutonic. This leaves sedimentary rocks as generally neptunian, but the word is no longer used because there are sedimentary rocks that are deposited on dry land, especially sandstones. Thus, one of the most popular terms in early geology has now all but disappeared.
Volcanoes are among the most spectacular of geological phenomena, but plutonic rocks are what end up forming the basic structure of continents. A "pluton" can be a large formation of plutonic rock, but plutonic intrusions can extend for hundred of miles, creating "batholiths," i.e. "deep rocks," which often form the massive roots of modern mountain ranges.
The processes that produce plutons and volcanoes make the rocks look different, and they also end up producing characteristic mineralogical differences. That the rocks look different means that plutonic and volcanic rocks can be distinguished with some ease even after geological processes have buried or exposed them and detached them from other kinds of evidence of their origin (like obvious nearby volcanoes). Thus plutonic rocks are "phaneritic," which means that crystals of the constituent minerals are large and evident to the eye, while volcanic rocks are "aphanitic," which means that crystals are only evident on microscopic examination. Both words come from the Greek verb φαίνω, phainô, which means "to appear" (as in φαινόμενα, phaenomena, "appearances").
We get this difference because in magma, the fluid state mixes together the constituent minerals. As a magma cools, the minerals separate, are drawn to their like, and begin to grow into crystals. In plutonic rocks, magma cools slowly and the crystals have time to grow large. They can grow very large indeed in a very slow cooling pluton. The rock with the largest crystals I've ever seen (in my limited geological experience) was in the Black Hills of South Dakota. On the other hand, lava erupted by a volcano immediately hits open air or even water and begins to cool quickly. Crystals do not have time to grow to any significant size and so are invisible to any unaided inspection of the rock.
At non-explosive volcanoes, as in Hawaii, hot lava can be observed flowing out of volcanic vents -- this is the very liquid, easily flowing pāhoehoe lava. The surface of the flow immediately and visibly begins to cool. Lava can easily flow for miles only when the top layer actually solidifies and forms a lava tube, which then protects the remaining lava from solidifying in turn. Lava can cool so quickly on the surface that it does not crystalize at all but forms a glass, which is a solid but whose structure is still that of a liquid. Obsidian is a volcanic glass. From the Hawaiian volcanes, we also get 'a'ā lava, which is rough, rocky, slow moving, and piled up. The name is derived from 'ā, "fiery, burning." If that is headed for your house, you have time to get out. But there is no stopping it.
The mineralogical
| Plutonic | Volcanic |
|---|---|
| Granite | Basalt |
However, we cannot simply say that plutonic rocks are light in color and volcanic rocks are dark.
| Plutonic | Volcanic | |
|---|---|---|
| Silicic | Granite | Rhyolite |
| Mafic | Gabbro | Basalt |
which contributes its name to an old Nevada mining town near Death Valley, at right, with the ruined bank building). And there are dark colored plutonic rocks, like gabbro. As it happens, rhyolite has the same constituent minerals as granite, as gabbro does of basalt.
So does this mean that light and dark rocks occur randomly as plutons or lava? No. Despite the counterexamples, the initial impression of light/plutonic/granite and dark/volcanic/basalt does go back to a deep affinity between the types. The affinity corresponds to profound differences in the Earth's crust. The crust under the oceans is largely basaltic, while that under continents is largely granitic. What goes along with these is another characteristic of the minerals. Granite is composed of materials that are lighter than those of basalt -- not just lighter in color but also in density. Continental crust is therefore less dense than is that under the oceans.
This is why the continents literally ride higher than the sea floor. They're floating. Despite popular stories about Atlantis sinking beneath the waves, or California falling off into the Pacific, these events are impossible. Continents can be eroded, broken up, or mashed over millions of years, but they cannot sink. Quite the opposite. The Sierra Nevada Batholith, which formed deep in the earth in the Mesozoic, has subsequently floated up, helping to raise the Sierra Nevada mountains in California.
The weight and color of basalt is due to the inclusion of magnesium and iron in its constituent minerals. Granite is light in color and density because it has little of those metals and substantially consists of aluminum and silica, i.e. silicon dioxide (SiO2), which in its pure state is the mineral quartz -- familiar window glass, a glass of quartz, is generally made from sand, which is largely weathered grains of quartz.
Granite is oversaturated with quartz and thus typically has pure quartz crystals in it. Rocks like basalt get called mafic from the magnesium (Mg) and iron (Fe) in them. Rocks like granite get called silicic or sialic from the silica and aluminum (Al) in them. But basalt has silica in it also, just in a very different form than in granite. Indeed, oxygen and silicon are the two most abundant elements in the earth's crust. The story of the rocks of the crust is thus paralleled by the story of silica.
It is now thought that the mantle of the Earth, the whole area between the crust and the core, consists of a rock that, where we can find it at or near the surface, is called peridotite. Peridotite contains from 40 to 100% the mineral olivine. If it contains more than 90% olivine, it is dunite. These are ultramafic rocks (perhaps dunite is ultra-ultramafic). Olivine thus looks like one of the most basic, or most primitive, minerals that underlies the Earth's crust.
It is not just that olivine contains magnesium and iron; silica occurs in olivine in a unique and simple form. Silicon dioxide, SiO2, is electrically neutral; but in olivine we get silicon surrounded by four atoms of oxygen, which between them would account for an ionic charge of -8, with carbon only balancing with a charge of +4. 
Thus, we get a molecule that becomes the negative ion (SiO4)-4, the silicate anion. The oxygen atoms group around the silicon atom in a tetrahedron. See the discussion elsewhere for the coordination numbers produced by the relative sizes of such atoms. The silicate anion can be neutralized by two magnesium, Mg+2, or two iron, Fe+2, cations (positively charged ions), or some mixture of the two. The olivines thus form a series from forsterite, Mg2SiO4, to fayalaite, Fe2SiO4, with a range of percentages of each in between. The olivine series thus can be written, (Mg,Fe)2SiO4.
Olivine is characterized by its independent ionic tetrahedron. Tetrahedra, however, can begin to link together as oxygen atoms begin to share silicon atoms and thus form corners of two different tetrahedra. If we get a single chain of tetrahedra, each one linked to the next, we get minerals in the pyroxene group, where the ratio of silicon to oxygen is Si2O6. A single chain can form a ring, as in beryl, Be3Al2(Si6O18). A double chain, were single chains link together, gives minerals in the amphibole group, with a ratio of Si4O11. And the silicate tetrahedra can link together into a continuous sheet, which characterized minerals that are clays and micas, Si4O10.
As oxygens are eliminated, we are approaching a limit. In olivine, the ratio of oxygen to silicon is 4:1, in a pryoxene (or beryl) 3:1, in an amphibole 2.75:1, and in a clay or mica 2.5:1. This is approaching the 2:1 ratio of SiO2, true silica, which will exist in the framework silicates, where the oxygen atom at each corner of the SiO4 tetrahedron is shared by another tetrahedron in a three-dimensional structure. Since this is electrically neutral, it can exist in pure form as the mineral quartz.
Peridotite is olivines mixed with pyroxenes or amphiboles. Dunite can be nothing but olivine and pyroxene. This already suggests a certain hierarchy. As the olivine-rich materials rise into the crust as magma, they begin to evolve. Perhaps not at first. Hawaiian volcanoes erupt a lot of olivine -- if the pure mineral erodes out, it can even form a green sand beach. If such materials are buried, however, or subducted into the depths, under either an oceanic or continental plate, the material is reheated under pressure. We can easily imagine the silicate tetrahedra begin to link together in greater numbers. The olivines evolve into pyroxenes, amphiboles, sheets, and framework silicates. As each of these approaches closer to electric neutrality, it needs fewer positive ions and thus become more silica rich, which means lighter and less dense.
Now there is a clue about the relationships between granites and continents, basalts and oceans. Oceanic crust is young, produced at mid-ocean ridges. It is straight out of the mantle. Hawaiian lavas are the newborn rocks of the earth. Continents, however, have a history. Granite is the result of the reworking, perhaps the multiple reworking, of previous crust. When an oceanic plate is subducted, as under Japan or the west coast of South America, basalt and water is carried down to the depths. It melts and rises towards the surface. The silicate materials, however, are lighter and rise faster. The magnesium and iron are heavier and may rise more slowly or even settle. With pressure and the loss of positive ions, the silicate tetrahedra can link together.
Thus, when a volcano erupts in the Andes, it is no longer with the same mafic materials that were drawn down under the continent. It may erupt andesite, which is quite close to basalt in composition, but lighter and with more silica. A magma that finally has the same composition as granite can erupt as a rhyolite. This may also happen where continental crust meets continental crust. Nothing gets subducted there, but the granite rock is pushed both down and up by the force of the collision, as is happening right now where India, which used to be an island, meets Asia.
Silicacious magmas are more viscous than mafic ones. The vents, pipes, and dikes (cracks in the rock through which magma flows) tend to become blocked with the magma, whose pressure then builds until there is an explosion. Mature continental volcanoes thus tend to produce catastrophic and dangerous explosive eruptions. Vesuvius or Mt. St. Helens erupts, and you better be running (but it may be too late). On the other hand, Kilauea erupts, with its more fluid and less explosive basaltic lavas, and people arrive to look at it. No one is quite certain what any volcano will do, however, which is why even volcanologists sometimes get killed doing their job.
But if there is an evolution in the reworking of the silicates, there is also an evolution in the framework silicates themselves. Pure quartz is pure quartz, but the most common mineral in the Earth's crust, and on the Moon, is quartz with certain impurities, namely feldspar. Besides color, density, and silicate structures, granite and basalt are also distinguished by different feldspars.
Feldspar is basically quartz, SiO2, where some silicon atoms are replaced by aluminum atoms. Since aluminum ions will only have a +3 charge instead of the +4 charge of silicon ions, the -2 oxygen ions will result in a net surplus negative charge, i.e. (AlO2)-1. This then attracts positively charged ions. In feldspar, these will be potassium, sodium, or calcium. Silicon +4 ions themselves are only 0.39 Angstroms in diameter, and aluminum +3 ions 0.51 Angstroms, so both of these arrangements make for the same tetrahedral (4x) coordination with oxygen.
Since potassium and sodium are chemically similar -- they are alkali metal elements -- and tend to form singly charged ions, K+ & Na+, while calcium is chemically somewhat different (an alkaline earth) and forms doubly charged ions, Ca+2 (which means that we need two aluminum atoms for two silicons, unlike the one for three with potassium and sodium), 
we might expect potassium and sodium feldspars to be chemically different from calcium feldspar. However, this is only part of the story.
Potassium feldspar, KAlSi3O8 is relatively distinct as Orthoclase ("straight break" in Greek), while sodium, NaAlSi3O8 and calcium, CaAl2Si2O8, feldspars form the Plagioclase Series ("slanting break" -- both names describe characteristics of the crystals). A smooth transition occurs from pure sodium to pure calcium in plagioclase, with similar crystal structure. From sodium to potassium we do get the Alkali feldspars, but these form a continuous series only when formed at high temperatures. They therefore do not make as natural a unit as the Plagioclase series.
The key to this peculiarity of the mineralogy is the size of the ions. 
The potassium ion is very large, at 1.33 Angstroms, while the sodium and calcium ions are not only smaller, but of similar size, 0.93 and 0.99 Angstroms, respectively (see discussion of the unit "Angstrom" here). With the O-2 ion at 1.40 Angstroms, potassium ions will form cubic (8x) coordination, as at left, but sodium and calcium ions will form octohedral (6x) coordination, as at right. This produces crystals with different structures, which can be distinguished by simple inspection.
As it happens, basalts and gabbros prefer calcium and granites and rhyolites prefer the akalis. An intermediate plutonic rock, with elevated calcium and reduced silica from grainite, is diorite. Why calcium tends to stick with the more mafic minerals, I do not know. Calcium becomes an important element in continental rocks as it is used by organisms and deposited as calcium carbonate or calcite, CaCO3, in limestone. With some magnesium thrown in we can get dolomite, CaMg(CO3)2.
Thus, beginning with the difference between Plutonic and Volcanic rocks, we are led into various issues of mineralogy and the evolution of the earth. The details go on from there. After all, granite itself is a mixtures of minerals -- feldspar, mica, and quartz. We can have different feldspars and different micas, which means that granites can look rather different from one to the other. Biotite mica is black, while muscovite is white. The feldspar in granite can be pink, as in the granite from the Llano Uplift in Texas (with biotite), which is used in Texas government buildings and elsewhere. Even quartz can have different colors from different impurities. In the Black Hills there are marvelous beds of pure pink quartz.
A little geology can go a long way. As child, I loved the drive up US 395 and US 6 into the Owens Valley in California. Before I lived in Hawai'i, the last time I drove through the Valley was in 1971. It wasn't until the early 90's that I got back. When I did, it was a revelation. The lava flows and cinder cones, some of them red, were unmistakable. It was a world that had previously been invisible, but it is difficult to live in Hawai'i without learning about these features. And all of this, of course, was with the great Sierra Nevada, and its massive granitic batholith, off to the west. Questions like, "Why is there volcanic activity east of the Sierra?" cannot even be asked if the features cannot be recognized. The answer, of course, is something else -- the place to start may be John McPhee's great Basin and Range [Farrar, Straus and Giroux, 1982].
Periodic Table of the Elements
Philosophy of Science, Geology