A democracy and a republic are the same thing. So it definitely confused me at first that the two mainstream American politic parties, the Democratic party and the Republican party, have basically the same thing.
They sound pretty much exactly the same because they are pretty much exactly the same. The differences between the two major parties are relatively minor, such as democrats being slightly more favorable towards things like abortion or gay marrriage than republicans, although even these aren't universal (There are both pro-life democrats and pro-abortion republicans, as well as folks on both sides who have their own opinions of gay marriage). For the most part, these differences only make very minor differences in the lives of the citizens, and neither party is for example advocating monarchy, or nazism.
Part of the problem comes from the whole "Liberal/Conservative" thing that has pretty much been imported straight from the UK, where the parties actually were called that. The ideologies behind the parties aren't really this simple, and The ideology of "American Conservatism" is actually called "Classical Liberalism", and "American liberalism" is actually called "Modern Liberalism".