I hope this thread garners some other responses, because I'm not entirely sure either. I'd love to get some other opinions/versions.
Through most of my riding education, I just heard and used the terms two-point and sitting. I vaguely remember someone making the distinction between two point and three point - two points of contact with the saddle - your knees; three point, your knees and crotch, but *not* your seat bones, which would be full seat. (I just edited my above post to reflect what I just said, I had to think throught the rationale of the names.)
I also assumed that half seat and two point were the same and interchangable; but I'd love to hear from others. I'd also love to know if anybody else has heard or been taught the distinction about three point contact.
As far as standing in your stirrups with your crotch in front of the pommel and laying on the horses neck; that's just bad, incorrect riding and doesn't need a special term.