The Sith line was broken up many many times.
Initially, there were Xendor's minions who fled, one of which we know as Ajunta Pall. These arrived on Korriban and other worlds, and subjugated the Sith race, interbreeding because the natives had impressive Force potential.
The empire these rogues made culminated in the ancient Sith Empire, and was more or less destroyed thanks to Sadow's machinations. After this, the Sith were scattered and hunted by the Jedi. I believe I recall a timeframe of up to a decade and a half where they were still fighting. In any case, the ancient line was broken. No true blooded Sith remained, and the half bloods were likely dead as well.
Freedan Nadd, a rogue Jedi, finds evidence of the Sith Empire and becomes Sadow's apprentice. He kills his master and molds his own kingdom on Onderon. He rules as an open god-king, and his dynasty continues to perpetuate the dark side but never expands. Nadd hates the Jedi, but really the Jedi never come into contact with him or his kin until Arca Jeth arrived with Ulic and others. Nadd's descendants successfully corrupt Ulic, but the next real Sith Lord is actually Exar Kun, who takes the remnants of Sadow's works and attempts to rule the galaxy.
You can see clearly how the methods of the ancient Sith contrast the Nadd dynasty, and then Kun. After Kun, we have Revan and Malak, who are more military men. Revan's been said to be more of a good guy masquerading as a Sith Lord, and his intent is thought to be the unification of the Republic under the Sith to protect against an outside force. In this, he's less trying to be a god-king absorbing power for its own sake than he is trying to be a military figure using unsavory tactics. Malak differs from his master in that he's an idiot. Sorry, not glossing that one for you, folks.
After Revan, we have the Sith Triumvirate with Sion, Nihilus, and Traya. They each have separate goals; Sion hates the Jedi but cares nothing for ruling the galaxy. Nihilus is consumed by hunger, and Traya wants the death of the Force. They are hardly heirs to the ancient Sith or Xendor.
After this, all seems rather quiet until the Brotherhood is formed. They're more akin to a religious warrior community than an empire of sorts, and they wage open war against the Jedi until Bane comes into the fold. Bane then remakes the Sith Order into a shadow organization, and it's assumed to disappear until Sidious comes out of the dark closet (no pun intended) and rules openly as a master manipulator.
So really, you can say it's "one line", but that's not an accurate representation of the shifting ideals and structures of the Sith legacy. If anything, the Sith have shown to be much more versatile and adapting than the Jedi.