I can understand the difference, actually (even though semantically there may not be one). A parallel universe is just a different reality that does not necessarily result from a branching from the "prime" universe (like the Mirror universe, although I heard that in some versions the point of divergence with our own was actually identified), while an alternate reality is a universe created from an alteration to the past (like the universe with an assimilated Earth glimpsed at the beginning of Star Trek: First Contact).
So this would mean that the universe into which Spock and Nero arrived was not the past of the "main" Trekverse (which would explain the bigger ships, the different aliens, the more militarized Starfleet, and almost everything else). Fine by me
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett