I certainly don't have the experience and knowledge in tractors that Mr. Shaeffer has, but from all the reading I've done the past few years on all the different tractor forums, sites, etc., I must take exception.
I understand the three types are as follows (and makes sense to me anyway):
standard PTO: driven off the transmission, will turn when clutch pedal is out (engaged), will turn when clutch is in (disengaged) but tractor is coasting (bushhog pushing the tractor problem), will stop when clutch is in and tractor is not moving.
live PTO: commonly the two-stage clutch version where the clutch is pushed in (disengaged) part way which disengages the transmission but not the PTO, and when pushed in all the way disengages both the tranny and PTO. I think the Allis CA was one of the first in '51(?) with the ability to engage/disengage the PTO separately from the tranny but had a separate hand lever (maybe a crude version of Independent PTO?).
independent PTO: separate lever, switch, etc. that was in no way connected to the tranny...in other words "independent." Could be hydraulically actuated and driven, electrically actuated and mechanically/hydraulically driven, or mechanically actuated and driven.
Or, I could be wrong! in which case, please enlighten me!
Bill in CO