The word "possible" needs its counterpart "impossible" to obtain any meaning. Possibility is always and only relative to some set of restrictions. There is no such thing as possibility per se. A "logically possible" world is a world that doesn't contradict the laws of logic. What about a world where the laws of logic won't count? Such a world is certainly not logically possible, but it might be a possible world relative to something else than classical logic.
A "mathematically possible" world does not contradict mathematical laws, but here one has to make clear what set of mathematical axioms those laws are based on. There are mathematically possible worlds with the lemma of Zorn being true, and others where it is false. There is a mathematically possible world without addition, with just the axiomatic foundations of addition denied and all the more basic axioms left intact. But that doesn't mean that in that world addition is impossible. It's just not there. Now, a "physically possible" world is a world which is possible relative to some set of physical laws. It might be the set of physical laws that is valid in our world, but it also might be some other set of laws. Since physical laws are something else than logical laws, the physically possible worlds are not equal to the logically possible worlds.

This all has nothing to do with the Everettian multiverse. In fact, the Everettian multiverse is a very restrictive set of physically possible worlds. For example, it does not contain the worlds where Bohmian mechanics is true, although the Everettian as well as the Bohmian worlds describe the same quantum phenomena that we observe in our world (at least in the non-relativistic domain). So maybe they are not even distinguishable by any observer. (This is a matter of strong controversy, though.)

Moreover, the physically possible worlds and the Everettian multiverse have nothing to do with the parallel universes conceptualized in kosmology, which are something else entirely.