The term "parallel universe" is more general, without any connotations implying a relationship, or lack of relationship, with our own universe. A universe where the very laws of nature are different – for example, one in which there are no Laws of Motion – would in general count as a parallel universe but not an alternative reality and a concept between both fantasy world and earth.
The actual quantum-mechanical hypothesis of parallel universes is "universes that are separated from each other by a single quantum event.