Dave,
I hope I can help, but don't expect it to be 100%, I hope someone will pick me up and correct it.
This is for parallel reamers only.
Hand Reamer
Will have a square end on it, so that it can be turned with a tap wrench.
Can be straight or spiral flute. Straight is usually for deeper holes, spiral for shorter holes or plate.
Normally, there will be a rather long lead taper on it. So the reamer has to penetrate thru the hole by at least the taper length, or else you will end up with a tapered hole. I personally have never come across a bottoming hand reamer, for use in blind holes, and so has no lead in taper, but they might exist.
Machine Reamer
Can have almost any shaped shank, either plain straight, or morse taper. They will not have a square drive end on them.
Normally they have only a very small or if a bottoming reamer for a blind hole, no lead in taper.
The cutting heads come in all shapes, depending on the use they are made for.
Chucking reamers, as far as I can understand are just another name for a machine reamer, and have just plain shanks for holding in a drill chuck.
The sets of adjustable reamers you can buy are for hand reaming only. There are some machine adjustable reamers, but are a totally different and more robust design.
Hope this explains a little towards what you need to know.
Bogs