It seems the questioner is actually asking the differences between republic and democracy, neither of which has anything to do with the Republican or Democratic parties here in the U.S. As already stated, and broadly speaking, Republicans core belief is smaller government and lower taxes, while Democrats defend bigger government and the programs that go along with that as well as higher taxes, at least on the rich, so to speak.
While a Republic is actually the description of the type of government here in the U.S. A Republic elects representatives to vote on governmental matters, while a true Democracy has the individual voting directly on any given matter before governement. In any nation of much size, that becomes quickly unworkable...