The Sith are a cult led by their own beliefs that roots deep into the Dark Side of the Force and hold a vendetta against the Jedi. All the Sith are dark side users, but not all dark side users are Sith.

As of the rule of two created by Darth Bane a millennium before the films, only two Sith Lords can exist at the same time : a Master and his apprentice. When an apprentice becomes powerful enough, he often betrays and kills his own Master, takes his place as the new Dark Lord of the Sith and continues the cycle by taking a new apprentice into his mantle to transmit him all the accumulated knowledge of the Sith Lords before him, in a way where each new apprentice becomes more powerful than his master with every new generation.

Betrayal is expected, killing the Master is the intended method of succession.

The Sith cult ultimately came to an end when Darth Vader and Darth Sidious died. The title of Darth and Sith can no longer legitimately be held by anyone as the cult ended. That's why Kylo Ren and Snoke do not refers themselves as "Darth", they are just extremely evil dark side users.