Alternate realities are built up out of alternative concepts, concepts not shared by other intelligences. Some such alternative concepts are:
strong free will
survival of death
An alternate reality will typically not be built up entirely of alternative concepts. Some concepts will be shared across alternative models of the world.
The level at which a concept appears in the abstraction hierarchy is also important. A Christian's idea of love is rather different from a biologist's.
"When a pickpocket meets a saint all he sees are pockets." The pickpocket and the saint experience different realities.