The other poster is leading you in the right direction. Think of the live/dead issue in reference to the drive train.
If you have a single stage clutch, and a tranny or ground based pto.. then when you clutch the trans.. you lose drivetrain and pto.. both at once.
With a 2 stage clutch, you can clutch the drivetrain, and maintain a tranny based pto.
Some older tractors got around this by having a single stage foot clutch, but then also had a hand clutch that ( depending on model ) was more like an axle clutch... it had the effect of stopping forward motion.. but letting the tranny pto run.. thus giving you live power.... kinda like a split 2 tage clutch.
Later on you had independent pto... it was not connected with the drivetrain clutch, and thus your pto worked whether the main clutch was in or not as it operated off of it's own mechanical or hyd activated clutch.
Live pto is nice for things like hay bailers.. where you may need to stop to let the machine clear, without the machine stopping, as would be with a non live pto.
A live pto via 2 stage clutch or independent, also will no transmit rotary inertia up the driveline to a tranny based pto like a non live pto will.. ( brush mower than is able to push the tractor via pto to driveline hookup.. even with clutch pushed... which is why the ORC ( over running coupler ) was made. Many unscrupuless or ignorant individuals will sell ORC's claiming they make your single stage clutch tractors have 'live pto' when in fact they do not.. it just decouples the rotary motion when the implement is turning faster than the tractor pto stub..
Soundguy