Those are more what I'm refering to, myself. Different "big bangs" with entirely detached realities. I'd say they're more likely to exist than not, but presumably we could never detect them unless they can "collide" with ours.
The many worlds of QM aren't different big bangs. They would all share the same singular big bang. They have separate futures but the same past, at least from the point that they branched (this makes me wonder about time reversal symmetries, but never mind that).
The mathematical universe idea would include completely spatially disconnected big bangs, as well as mathematical structures that don't even have spacetime, let alone big bangs.
The idea of other universes colliding with ours also comes from string theory, in which our 3+1 dimensional spacetime exists sort of stuck on a d-brane in a higher dimensional space. There would be other d-branes moving independently through that higher dimensional space. Note that the distance between us and them is real distance, just though a different dimension which we don't have access to. This fits most closely in the level 1 or 2 multiverse, but I do admit that the additional dimension and the possibility of a collision makes it slightly different.
Anyway, all of this, while I find it very interesting is beside the point, which was that there are regions of space that we know exist but whose specific features we cannot know. We know those features exist but we can't know their specifics.