Kinda interesting question since I long ago learned to put the butt of the rifle centered in that "pocket" between the shoulder and the collarbone. So that's what I would consider to be an "armpit hold."
But before I got an AR-style rifle I had been noticing that photos of folks shooting it held it with the toe of the stock held high up near the point of the shoulder. When I finally got one just because I wanted to find out what all the AR fuss was about, I found myself holding it the same way, toe of the stock near the point of my shoulder. (Definition: To me, the "heel" of the buttplate is the top part, the "toe" is the bottom part.)
That was OK with the light recoil of that puny little varmint cartridge the AR-15-ish rifles use, but I felt that if a more powerful cartridge were used, as in the AR-10-ish rifles or a conventional deer rifle, that would tend to hurt a bit.
So I guess the term "armpit hold" is the way I hold a conventional rifle, to absorb recoil, and the "not-armpit hold" (or maybe "point-of-shoulder hold") is the way one holds the AR-style rifle.
Am I on the right track here?
Terry, 230RN