Like the Rakata, the Sith had a basic grasp of the Dark Side. The planet Korriban is strong in the Dark Side and the Sith were able to harness it to use Sith Magic and Sith Alchemy. The original monks discovered The Force on Tython, but The Force is everywhere. Much like the Rakata had the Dark Side in their technology, the Sith had the Dark Side in them. Many Sith were strong in The Force. Adas weeded out the weak so only the strong ruled.
The Sith'Ari is the Dark version of The Chosen One. A Sith that would destroy the Sith and recreate them stronger than before. Adas was the original Sith'Ari, the chosen being. He was considered perfect (a prerequisite for the Sith'Ari), but this was before the prophecy of the Sith'Ari. After Adas died the priests prophesised of a new Sith'Ari that would destroy the Sith and recreate them stronger than before. Darth Bane was that Sith. Bane was the true Sith'Ari, Adas was a prototype so to speak.
PS. Does anyone know what Sith'Ari means in the Sith language?
IIRC Bane didn't consider himself the Sith'ari. He simply decided to make himself the Sith'ari.
I think what we see here is simply a change of meaning of the word. Sith'ari originally meant something different in King Adas time than it did later. Just like the word messiah originally simply referred to a king (who was made king by being anointed). Was Adas the first Sith'ari or could it be that there have been others before him?
I've read somewhere that, translated literally, Sith'ari means "perfect being".
P.S. Darth Ikoral can trace his line back to King Adas. Given the amount of time, though, it is not unlikely that almost every Sith Pureblood is somehow related to King Adas.