Okay, we know squeeze happens because the air in the suit is compressible. That being a given, let's examine the mechanics of a squeezes.
To understand drysuit (or glove) squeeze, consider a ridge in the waterproof membrane of the suit. That ridge can be thought of as a flexible bag of air. When you increase the pressure (say, by descending), the volume of air in the ridge naturally should decrease proportionally.
For the early part of the squeeze, the "top" of the ridge (i.e. that portion farthest from the diver) can collapse in on itself. The ridge gradually collapses from an inverted V (or U, if you will) to more of an inverted Y shape. As the "open" end gets compressed smaller and smaller (closer to a T shape), more and more fabric is taken up by the pinched-together end of the Y. As you near T-ness, you can collect enough fabric in the closed portion of the ridges to the point that there is not enough open fabric left to comfortably encircle the diver -- you've basically "taken in" the fabric to make a much smaller suit, so you're squeezed by the suit constricting around you. (This is the classic "couldn't breathe" squeeze.)
Of course, since the material is not perfectly flexible, at the limit of its collapsibility, you can arrive at a condition where the "inside" (perhaps of one of those Y-fold ridges) is constrained from collapsing any more, which turns it into a small fixed volume (instead of the variable volume it had been prior to that point). As the volume is now fixed, the pressure is as well. The pressure against the inside of the tissue pressed against it, however, is (to a reasonable precision) the ambient pressure at that tissue's depth. In the interest of convenience, you can consider this a partial vacuum "pulling" on that tissue -- your skin, for example. (This yields the classic "drysuit hickey" result of a bad squeeze.)
So, basically, you start to feel the pinch squeeze because of the suit pressing in on you as it's taken in by the Y-ridges, and you get the big drysuit hickeys as you take it far enough that the suit has collapsed to the point it becomes a rigid body and creates small local areas of "partial vacuum". Both sides can be correct.