I'll also add a bit of confusion to this.
I was always taught (Huntseat/Equitation) that 2-point was like the last example photo posted from Practical Horseman. In lessons, my trainer would also call for 'Horizontal close' and 'Vertical far' positions. Horizontal close being the position of a rider over a jump -- hands up on crest, body horizontal (parallel?) to the saddle/horse. And vertical far was basically standing up in your stirrups, straight up and down.
Of course, I haven't heard it referred to that way since he taught it to me, so maybe it was just something he came up with?
With all the various names for positions everyone's mentioned, I wonder if it has something to do with the disciplines maybe? Just a thought.
(I'll have to ask my trainer what she thinks about it. We always end up having mini discussions on how jumpers vs. hunters approach jumps, different hunter styles, etc.)