I would say that the overturned Spin is a very different beast than the basic spin, because it's not just a matter of a little more or less rotation. It turns it into an entirely different movement -- steps are described differently, different technical execution, and with different figures to follow. In fact, the overturned spin is almost exactly halfway between a normal Spin Turn and a Natural Pivot, or maybe just a hair closer to the pivot, beleive it or not.
There's also something that's been coined a "Running Spin Turn", but it's not really a Spin Turn at all. It's one pivot (count "1") followed by 1-3 of an Open Natural Turn (count "and 2,3").
Just about anything resembling or containing Natural Pivots might be described as a Spin Turn of one sort or another, so it suffices to say that there are many possible variations of the Spin Turn. But as it is written in the book, there are basically three versions: Basic, underturned, and overturned (the overturned usually to be followed by a turning lock).
Sincerely,
Jonathan Atkinson
www.ballroomdancers.com