MWI is just one of multiple multiverse ideas. Most multiverse ideas (like Tegmark's Levels I, II, and IV) are basically what-if ideas without any direct evidence, but MWI specifically happens to be a more-grounded idea based on trying to make sense of what the (well-tested) Schrodinger equation says about reality.
The first part of your description of MWI ("The many-worlds interpretation of quantum mechanics imagines our universe as one node in an infinitely branching tree of universes where every possible quantum outcome exists in its own universe.") is pretty good, if a slight though common simplification (different branches aren't entirely separate, so envisioning it as a tree is only mostly correct; different branches can sum together or cancel each other out if their configurations are identical).
