The distinction between the two is one is an alternate reality, though I always considered NuTrek to be apart of Prime Trek. The fact Spock Prime didn't cease to exist after Vulcan's demise leads me to believe he could get back to his reality (if he had the knowhow).
Rick Berman's version of Star Trek is merely one
version of Star Trek, based
on Gene Roddenberry's Star Trek, but no more or less valid than Abrams' version, which is also based on GR's ST. To lump Berman's Trek spinoffs under the blanket term "Prime" implies it to be somehow more legitimate or "real" Star Trek than Abrams' Trek, which is nonsense.
And I don't even like Abrams' movies...