Sorry that I'm very late in this game, but here's my two cents about all this. Parallel universe and alternate universe can be distinguished, as seen above. But they could also be one and the same, at least in the realm of science fact. (Sorry if I'm posting this on a science fiction group.)
I'm having in mind the many-worlds interpretation and other multiverse interpretations in the field of quantum physics. In a nutshell, such hypotheses posit that all alternate or "what-if" histories, both that have already occurred and will occur in the future, take place in real life, just that they're in parallel universes or alternate universes. This way, "what-if" histories don't have to be restricted to the realm of a fictional alternate space in this universe - in other words, not restricted to the conditional, as in to the "could have been", "would be", etc. And multiverse theories could serve to reduce, if not eliminate, the suspension of disbelief in terms of alternate histories. It's possible that there's an infinite number of such universes in the cosmos.
Having said that, alternate histories or alternate universes could still be considered fictional, though often based on plausibility, in the sense that one can only approximate, based on real-life examples from our own universe, what such parallel/alternate worlds are like.