There are basically 3 types of PTO:
Independent has its own cluth completely seperate from the motion of the the tractor. You can turn it on and off with out doing anything with the foot clutch or motion of the tractor.
Live PTO has a two stage clutch. Depress the clutch pedal completely and the trans can be put in gear and the PTO lever moved to engage PTO. The first little bit that the clutch come up will get the pto spinning with out moving the tractor. Then the transmission will start turning as the second stage of the clutch is engaged. This type PTO allows you to get the implement spinning before the tractor starts moving. To disengage, the clutch needs completely pushed in, for power to stop going to the implement. The motion of the tractor can be stopped without stopping the PTO.
The original or transmission PTO on tractors like old H's or 8N Fords was completely tied to the movement of the tractor. These tractors have a single stage clutch, and the PTO is completely tied to the motion of the transmission. Engage PTO and put tractor in gear and they both start moving and spinning at the same time. Not the best thing for say running a mower since you cannot get it started before you start moving. This PTO can be used with the transmission in neutral if you need stationary power, but you have to work the foot clutch to turn it on and off.