Yup. After the Hundred Years Darkness war the surviving Dark Jedi were expelled from the Republic and they found their way to Korriban (or was it Ziost?) and enslaved the Sith race and became the Dark Lords of the Sith or something along those lines. Eventually Naga Sadow decived the Sith into thinking they were being invaded by the Republic when some travelers fornd their way to Korriban so Naga Sadow was probably the first "Sith Lord" to attack the Republic.
kinda sorta... not really. You're close, but there is alot more to it.
in the EU, there is a "jedi civil war" reffered to as "the rift" or "the division". Basicly, THOUSANDS and THOUSANDS and THOUSANDS ( like 10-15K years or so) of years back, the "light side jedi" and the "dark side Jedi" worked together. Those that used the light siade focues on drawing on the power of the universe, and those that used the dark side Drew upon the power of the self.
Those who used the poweres of the universe had a very Zen-like existances, and those who ued the poers of the self were very... passionate. the problem was that in manny cases the useres of the power of the self would become unstable. As such, the jedi council ( generaly made up entirely of "light siders") Decides to abandon the teaching of the way of the self, and outlaw it. this is what spark a war between the two factions, which eventualy leads the "dark jedi" to being driven off ossus, and out of the galaxy.
the dark jedi eventualy come to the parts of the galaxy controled by the sith race. The sith race practieced use of the dark side of the force, Alchemy, and "sorcery". the sith culture Has been descrived as a fairly...agresive group of people ( think Klingons, without the honor mentality) Over a few thousand years the Dark jedi and sith Cultures slowly shared ideas and intermingleld untill both cultures beacme one. same ideals, same practices, same everything. One of the few constats was the hatrid of the jedi. the Dark Jedi's unfair treatment at the hands of their opressors, etc etc etc.
At which point Naga Sado steps in and does his thing, and the rest is history.
Funny thing, Naga Sadow in the long run regrets doing this.