The story of WAAPT spans a rather large multiverse, and while most events take place in one of them, others occasionally come into the spotlight. Here are some that have:
Original timeline: The universe where most of the RP takes place. Also known as the OU, or Original Universe.
Alternate Timeline or AU: A "darker and edgier" alternate universe split off from the OT by the legendaries due to the actions of Cyrus.
Another Universe: A "lighter and softer" alternate universe with many differences from the OT. Also known as the Other or Another Day Universe.
PMD-A: The universe of the Pokemon Mystery Dungeon games.
PMD-B: A post-apocalyptic branch-off of the AU where humans are virtually extinct.
Netherworld Universe: Not much is known about this universe.
No Moon Universe: A universe where a Poison-type legendary is fighting its way back into canon against a Nidoran.
687th Parallel Universe: Not much is known about this universe (not even whether it's really the 687th) other than that the resident Arceus is very poor.
Giant Sea Creature Universe: A universe overrun by giant aquatic Pokemon.