After the debacle that was the Battle of Coruscant, the remnants of the Republic's military and citizenry separated themselves into two distinct groups: the "Alliance to Restore the Republic" and the "Galactic Empire".
Yes. The Rebels are in all six films. The Empire isn't seen until Episode II, though. It was formed some time between when the first film and the second film take place (25 BBY and 21 BBY, respectively).
For four fiery years these factions worked together to crush the clone menace, even while holding starkly-differing views on what the post-War galaxy should look like.
The Alliance wanted a constitutional, representative government composed of equal parts all known sentient species. The Empire demanded Human supremacy and loyalty to its supreme leader, Palpatine, above all else.
How the Empire won, at least until the events of the OT, is one of the major stories I am trying to tell in my prequels.