Eric, I know of 3 types, but as Bird suggested, you will find more detailed information from the sites he listed.
1) Transmission driven pto. Found on older tractors like 8N Fords. Only works when clutch is out. PTO speed varies with ground speed. Can be used stationary. A real pain in the butt for mowing, but I did it this way for 10 years. Over-running PTO adapter necesarry for some equipment like mowers with high inertia. In this case, when you push in the clutch, the inertia from the mower will still drive the transmission, and can push you into fence or ditch, thus an over-running PTO adapter should be used.
2) 2 stage clutch. Came out in the late 50's on Ford tractors. Tractor has one clutch pedal but two internal clutch discs and two drive shafts, one for the transmission and one for the pto. Push the clutch all the way down, both disengage. Push clutch half way down, transmission disengages, pto stays engaged, allows you to change gears without disengaging pto. Clutch all the way up, tranmission and pto engaged. This is still available today on budget tractors. I am not as familiar with this type, never owned a tractor with 2 stage clutch.
3) Independant pto. I would say all HST tractors have this. Once pto is engaged, it runs at engine speed. Tractor direction and ground speed is indendant of pto operation. This is the cats meow. Works very well for mowing.
Philip
