As far as I can tell from the game KOTOR (Knights of the Old Republic) there were a bunch of dark Jedi that were expelled from the Republic. They hid on the Sith planet. The Sith were a race that studied the dark side, and the dark Jedi learned all of their secrets. They eventually raised an army and went to war with the Republic, but in the fighting all of the original Sith were wiped out, leaving only the dark Jedi who then called themselves Sith. Eventually through various wars all of the Sith were thought to be destroyed, but some went in to hiding and started the whole master/apprentice thing.
So to answer your question, in the movies anyone can use the dark side, but only the master/apprentice pair can be Sith, ie there are only 2 of them. In the games which were set waaaaay before the movies, anyone in the Sith army is a Sith, and the master/apprentice are at the top of the pecking order.