Pull up - palms face the body. Chin up, palms face away from the body. A flexed arm hang is basically a chin up that is held as long as possible. Otherwise they are identical.
Seems odd, because pull ups tend to be easier than chin ups - a lot less strain on the wrists.
That's funny, because as I always had it, chin-ups were with the palms facing the body and pull-ups with the palms facing away from the body. It would seem from the wiki article on chin ups
that the terminology is somewhat imprecise and can be used both your way as well as mine.
According to that same article, however, the Marines use the term "pull up" to refer to either interchangeably, so that still leaves me at sea about just exactly what a "pull up" means in this context.