Of course, the terminology is moot in the end. It's something alternate and that's what matters.
But I prefer the more modern way of distinguishing between an alternate timeline and an alternate universe because it feels more well-defined than the old model.
It also helps to clear a few things up in Trek.
for example:
Fluidic Space --> alternate universe
Mirroruniverse --> actually an alternate timeline (it's still within the universe that we know)
Well you can try to make up your own definition as much as you want (you are the first one that I have read that uses such a definition for parallel universe) - But don't expect us to follow it.
Just calling something a parallel/alternate universe does not mean that you imply anything about its origin. It could have been created at its own big bang, or branched off a few nanoseconds ago. The term is wider than what you want it to be. Just get used to it.