Alright, after another call to the DEC I think I understand better the two permits.
1) Farm Fish Pond Permit: Only for fully private property BOW. Allows for stocking and removal of fish outlined in permit. Immediate family and workers can fish in BOW without state fishing license.
2) Fish Stocking Permits: It is a more general permit that allows for stocking of fish in any body of water (including private property). Separate state fishing license is needed to fish.
You cannot fish in a NY BOW (even privately held) without a NY fishing license with the exception of the Farm fish pond permit.
Both permits will state what species of fish you can stock. If you would like to introduce a different species, then you need to "update" the permit to include it.
This has been an interesting learning thread that I didn't even know before I started.