Truth is, these three formats--or sub-formats--vary significantly from market to market. So, in a very real sense, AC--or Soft AC or Hot AC--is whatever you want it to be.
But, yeah, if you think of it as being a continuum using two axes--old to new... and down-tempo to up-tempo--a programmer can position or re-position within the general realm of AC depending on what the market gives you or takes away.
Adding or subtracting 40 or 50 tunes allows you to shade the format one way or another. Adding or subtracting 100 songs allows you to make a major shift without requiring a public "format change" announcement.
This is an enormous advantage on the sales & cash flow fronts. Instead of needing to throw out a large (if not large enough) audience and advertising client base and start all over--as in switching from Hip-Hop to Country, for instance--you can re-position an AC significantly with minimal disruption.
Some years back we had one of the major programming research outfits (Edison or Paragon or one of them) conduct a market study for an AC and they came back with a grid showing about a dozen-or-so versions of Adult Contemp--you know, Rock AC, Urban AC, Modern AC, et cetera. So it's not just the Soft/Mainstream/Hot tags. Lots of options with Adult Contemp.