The Republic has a different origin story. The galaxy was ruled by the bloodthirsty Sith aristocracy, until a gang of slaves learned the Sith’s secrets of the Force and used them for good instead of evil. In other words, the Sith Lords existed long before the Jedi Knights, and it was the Knights’ crusade against the Sith which proved integral to the creation of the Republic. How the Sith return to the galaxy after so many millennia is a key part of the tale told in SW:ATG.
That’s a damn good inversion of the Jedi/Sith backstory. I’m jealous I didn’t think it up myself. 😉