The wavefunction is exactly the same as "infinite worlds". The essential aspect of the Everett / many-worlds view is that the wavefunction is the complete description of reality.

The "worlds" are just approximate ways of slicing up the wavefunction which correspond to our sense of classical reality. They are clearly (and uncontroversially) identifiable if you run a simulation.

Ah that's a better explanation

The "worlds" are just points in the space that supports the wave. You can use any other name, if you prefer, but there seem to be an infinite number of them.

All quantum mechanics has notions of "points in space that support the wavefunction," but these are different from the "worlds" in MWI.

Seems like I have been misunderstanding MWI all the time. How are they different?