In this fantastic bit of MS Paint artistry, I've shown an S-trap and a P-trap. In my humble opinion, the only difference between them is the horizontal run between the top of the upflowing bit of pipe (defining the end of the trap itself) and the bend to where the flow goes downhill to the rest of the drain system.

Image source: Me! Copyright: Are you kidding?
Also, please ignore the sharp corner in the transition between the black circle and the red line in the P-trap example and assume, instead, that it's a smooth curve, as a store-bought trap would be, work with me here...
How long must that red section of pipe be in order for what is, effectively an S-trap, to be considered a P-trap?
My reason for asking is that I'm getting ready to do the plumbing for a new bathroom addition, and I need to plumb in the sinks which will be against an exterior wall. I don't want to put the drain line into the exterior wall and reduce my insulation there, so I want the drain to go into the floor. A floor-based drain would usually be served by an S-trap, but it seems those are no longer code legal.