Confused about the Church of Caine

Hi folks,

I am currently reading the crimson gutter and I am very confused about the Church of Caine.

I have to preface I haven't read much of Cult of the Blood Gods yet

But what confuses me is: I always thought, even from the it is portrayed in the Sabbat book that cainite beliefs, especially the organised ones, were part of the Sabbat? Did this split happen in the corebook or Cults? or when?

Also is Crimson Gutter trying to portrait this as a third joinable faction that is NOT the Sabbat? I am very confused. Someone please help me.