Who said that there are two types of hanging? The Death By Hanging is the intended method, with the knot to the side. However, unskilled hangmen can goof. If the knot slips, strangulation is the method of death, and that's why Hanged by the Neck Until Dead is put in. It's not that they are intentionally different methods--it's just one statement covers the unforseen.
There actually is a lot more about this topic in the literature recently, and it's amazing how detailed the memoirs of famous hangmen were.
IIRC it was the person who was filling in for Glenn Beck this morning. I don't recall his name.