It always seems to me, as a non-American, that there are four parties in the US, two within the Democrats and two within the Republicans. Compared to parties elsewhere, the US parties are very broad, which is a consequence of the system I guess.
It's actually quite complex.
Broadly speaking (and using the US terms) there are various streams of conservatives, moderates, a formerly factionalized but now mostly unified liberal grouping, and the progressive/reformers.
(Aka the pseudo-conservative classical liberals, the regular classical liberals, the social democratic classical liberals, and the reformers.)
The modern Republican Party can be broken down into:
Libertarians. To be sure they are a small force, and somewhat swinging to the Democrats over social issues, but they used to & usually vote Republican. Libertarians basically believe in a very small government, and being left alone. They are most common along the Rocky Mountain states and are one reason Democrats have seen recent success in that region.
Neo-conservatives. Ex-Democrats, they are basically neo-Wilsonians, believing that the spread of democracy by American might will result in a better world. The Iraq war has basically trashed their influence.
Business conservatives. At times they've run the Republican Party (post-Civil War until Teddy Roosevelt, after Teddy to the Great Depression) and are basically concerned with economic values—a pro-business Wall Street oriented thing. (Generally speaking these are the Republican moderates today—they don't care or are with the Democrats on social issues, and they're not wildly concerned by tax cuts although they do want them.)
Neoliberals. Related to the business conservatives, but without the corporate welfare and with a libertarian-ish emphasis on a smaller state. Basically the free market is the awesome for everything.
Main Street conservatives. These are the small town midwest folks concerned with balanced budgets, some concern for social issues (they're against abortion, but not rapidly so for example), a strong America, and so forth.
Social conservatives. Mostly in the South they have until recently been focused heavily on social issues (i.e. anti-abortion, anti-gay, etc…) but people like Governor Huckabee are trying to move them to consider the broader issues their faith should compel them to look at—the poor, for instance.
Progressives. What few who remain in the party are basically old Teddy Roosevelt voters who believe that the government needs reform, corporations have too much power, and the little people need help. They don't really take a liberal or conservative position, but generally rebel against failure. With Roosevelt that was too much corporate power, with Ross Perot they felt it was a bipartisan failure of both parties to address economic issues.
Liberals. Related to both the progressives and the business conservatives, these were basically the Eastern Wall Street establishment plus concern for the poor. All gone now, basically, since Rockefeller lost.
The Democratic Party is:
Progressives. As above. They supported Ross Perot in 1992, and Barack Obama is of this grouping which explains his support (progressive states—basically the Canadian border states—+ Southern states with large black populations). Please note some Democratic liberals—i.e. the activist online community—misuse "progressive" when they mean "liberal" (and when they really mean "social democrat") when in fact progressives & liberals are two very different factions in American politics.
Southern Democrats. When used in this sense it more or less means conservative (& usually poor) white southerners who didn't vote for the Republicans because they were Republicans. Again, mostly gone. See social conservatives, Main Street conservatives.
Liberals. Social democrats, common on the West and East coasts. (Note that once upon a time there used to be several different groupings. As the conservative factions splintered farther apart with success, so the liberal factions have grouped together with defeat.). Generally allied with the progressives since a "reform" position right now is inherently a liberal position, given the conservative tilt of governance.
Moderates. As with Republican moderates (what few are left, at this point) they basically come to a halfway point between whatever the dominant conservative and liberal battle of the day is.
Conservatives. Sort of the right-wing of DLC style New Democrats. Centrist, adopts some Republican positions, big corporate supporters. Post-1994 Bill Clinton Democrats, say.
That's the quickie version. But the long version is pretty cool, how new factions pop up, how some fade, and how they wind in-between the parties.