Where do you see three sorts with different behaviour? I see two, an unstable sort just named "sort" and a stable sort.
sort performs O(N⋅log(N)) comparisons and so does the stable sort, although to be fair it also promises to work (more slowly, O(N⋅log*2(N)) instead) if there's no scratch space.
We don't get to ask for the no scratch variant, so we can't count that separately.
And these big-O values are totally uninteresting because they're typical for every modern sort, when people announce a shiny new general purpose sort it has the same complexity numbers. Does your STL have it? Who knows, the standard doesn't specify.
And that gets back to my earlier point, Introsort, the typical sort you'd find in an C++ program today, is relatively modern, and C++ was standardised in 1998. So actually quicksort was often in a "complying" C++ stdlib because hey, that's good right? Well, no, Quicksort's worst case has O(n*2) so it's actually forbidden by the STL's documentation, but nevertheless it was shipped because for many real world uses it's fast.