From what I understand, falling to the dark side does not necessarily make you a Sith. A Sith is a dark side force user who accepts certain teachings, observes certain rituals, as well as aligning themselves to a certain historical legacy. Dark jedi lack the cultural background to be considered Sith. In a later era, after the Rule Of Two is instituted, Sith would often use Dark Jedi as pawns. A common way for a Sith Master to gain the loyalty of a Dark Jedi is stringing them along with promises of accepting them as their Apprentice.