It seems like "multiverse" is used to describe a half-dozen mostly unrelated things or more (just based on the contents of this thread) including among them many-worlds. But, for example, eternal inflation has nothing directly to do with relative-state formulation, nor mathematical universe, nor the "multiverse" where you consider that portion of the universe outside our cosmological horizon to be a separate universe (I wouldn't agree that it is, but apparently that's a thing).
Max Tegmark has put these ideas into a hierarchy of multiverses, where universes outside of the boundary of the observable Universe are a Type I multiverse, and the many-worlds of the relative-state formulation form a Type III multiverse.
