Here's my take on this. Older tractors (pre 50's) had non live pto. The pto was shifted into and out of gear. The pto only operated when the tractor clutch was engaged. If you stopped the tractor, the pto would stop. For stationary work, you shifted the pto into gear, the transmission into neutral, and engaged the clutch to start the pto.
When live pto was introduced, the pto was given it's own clutch. You simply engaged the pto with this clutch completely independent of the transmission clutch. The pto drive shaft was connected live to the engine, i.e. it was always in gear, but the output shaft was controlled by the pto clutch, regardless of the state of the transmission or transmission clutch.
Allis Chalmers had their own thing going on,so tthat's another story.