I can never explain this is in a way that doesn't make my head hurt but I'll try here
Old School PTO - PTO driven off transmission output. Basically if you are in gear, and the PTO lever is on, the PTO is connected to the rear wheel gear train. If you push in clutch AND are in gear, your tractor won't stop moving until the mower stops turning. May not sound too bad until you need to stop fast. An overrunning clutch in driveline allows mower to "spin-down" without driving PTO. Basically, overrunning clutch will allow mower to "spin-down" without driving tractor forward.
Independent PTO - You will have lever that will engage and disengage PTO - regardless of drive clutch position, whether the tire are moving or still, whether in or out of gear. This feature came out in mid-60's.
Live PTO - clutch will have two stages. Stages will not be readily apparent to the unknowing. If clutch pedal is full down, you will have no drive wheel or PTO function (in gear/out of gear. PTO lever on or off). As you release the clutch to the first stage, the PTO will engage (if the lever is on), but, at THIS point of clutch travel, even if in gear, the drive wheels will not engage. If you further release the clutch, if in gear, the drive gear will engage also. Also if your wheels are turning and the PTO spinning , you can push in clutch to the transmission stage and the wheels will stop, but the PTO will still turn. Fully depressing clutch will disengage wheel drive and PTO drive
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Overrunning coupler