I know the current consensus on the Historicity of Jesus is still that a historical Jesus (likely) existed. I also know that proponents of Christ Myth theory are often portrayed as holding the position that 'a historical Jesus did not exist'.

I was wondering, however, what exactly I should think of when I hear these positions. If I, for example, believe there was a person who did almost everything Jesus did, but he was called Mark, I would say that would be (relatively) irrelevant - I would believe in a historical Jesus. Vice-versa, if some Jesus existed but he had nothing to do with the stories, I would not believe it to be true.

What if we hold the believe that multiple similar characters existed but they were combined by later tradition? Or that a historical religious disruptor existed but most of the surrounding stories are not real? To me, the discussion sounds similar to the discussion on King Arthur (not per se on content but on positions).

I was just wondering, what is the best manner of thinking of these different positions? When are you a proponent of the Christ myth theory?

Edit: I may have messed up my terminology partially, thinking of mythicism and historicity interchangeably.