There are a variety of PTO engagement types. The three most common are "non-live", "live", and "independent".
Non-live PTO only runs with the clutch engaged. It is directly driven by the transmission input shaft. No input shaft movement, no PTO. Very early Fords, 8N and such had this design. It was crude at best. Push in the clutch to stop tractor movement and the PTO attachment stops turning. Also, another bad side effect, if running a brush hog for example. The spinning PTO shaft will propel the tractor forward until it stops turning if used without an "overriding clutch" on the PTO shaft.
Live PTO is what I believe you are familiar with. With engine running, tractor sitting still, disengage clutch, engage PTO with small lever usually on side of transmission. Some grinding might be heard if you engage the PTO gear before the transmission parts stop spinning. Some older Fords used a 2 stage clutch to get the "live" part. Push the clutch pedal down 2/3 of the way and the tractor will stop moving but the PTO will continue. Push the clutch completely down and both stop.
Independent PTO is engaged by an oil clutch inside the rear housing. This PTO is most popular and can be activated/deactivated irregardless of tractor movement or clutch engagement/disengagement. Has not affect on tractor movement. No push. No stopping because of clutch disengagement.
On my Ford this is accomplished with a double splined clutch assembly and double shafts coming out of the transmission front. The inner shaft is the transmission input shaft and is driven by the clutch plate. Engage clutch tractor moves, disengage clutch tractor stops, all with no affect on PTO. The outer shaft is splined into the pressure plate and turns anytime the engine is turning. This drives a shaft thru the transmission to the rear axle assembly where the PTO oil clutch is located.
For your tractor to be making a gear grinding noise when you try to engage PTO it is at best a "live" setup and requires the clutch be disengaged and all gear movement stopped before it is engaged.
With that said, engine running, transmission in gear, clutch disengaged and tractor movement stopped, PTO should be able to be engaged with the lever with no grinding. If it can't, then we have a problem.
If the tractor clutch is wayyy out of adjustment I guess it would be possible that the transmission main shaft keeps turning with engine running, transmission in neutral, clutch disengaged. But if that were the case it should be hard to get the transmission in gear with engine running, grinding, etc?