Actually several different games, the Star Wars Role-Playing Game takes players to a Galaxy Far, Far Away for original adventures during the Rebellion Era (the original trilogy), the Clone Wars (the prequel trilogy), the Imperial era (the time between the trilogies), or in a host of other times leading up to or after the movies. Sometimes the movie heroes show up in the campaign, sometimes they are on the fringes of it, or maybe they won’t appear at all.
The first version of the game was published by West End Games from 1987-1999 and used the D6 system. There were over 140 sourcebooks and supplements which added tons of new background material to the Star Wars Universe, which was previously limited to the movies and their novelizations. Their material was so extensive that it was provided to Timothy Zahn when he began writing the Thrawn Trilogy which kicked off the entire Expanded Universe.
The second version of the game was published by Wizards of the Coast starting in 2000 using the D20 system and running very much like the Dungeons and Dragons 3.5 Edition. In 2007 they introduced the Saga Edition of the game intended to streamline the rules system.
The current version of the game was produced from 2013-2020 by Fantasy Flight Games and “consists of different standalone cross-compatible games where each one is a separate themed experience.” These games consisted of Star Wars: Edge of the Empire for 2013, Star Wars: Age of Rebellion for 2014, and Star Wars: Force and Destiny for 2015, while releasing Star Wars: Edge of the Empire Beta and Star Wars: Edge of the Empire Beginner Game later in the same year. They used the narrative dice system of the Warhammer Fantasy Roleplay 3rd Edition.