Here's my take:
Perhaps the early "Jedi" were mystics in less civilized systems. In the more advanced population centers closer to the core Force-users were not as visible. Gradually over time, governments of the less civilized systems began to formally recognize their powers. Hired on as advisers, these mystics began to refine their understanding of the Force and the powers they came with it. As their roles expanded into diplomatic and security responsibilities (much like samurai), their exposure increased. A few minor wars and skirmishes, where their involvement proved decisive, accelerated this notoriety.The Republic, recognizing their benefit, created an Order, with a physical presence located on Coruscant. Here their diplomatic and military skills could be exploited to the Republic's advantage. In return, the Order was given a haven to learn more about the living force, embark on missions to recruit others, and help bring peace to a confederated galaxy. As the organization matured, a rift occurred over (FILL IN THE BLANK). A detachment of force-users broke away and formed a independent group. Bereft of exposure to the accumulated wisdom and training provided by the Order, these force-users succumbed to the dark side and called themselves, Sith.