Many bird farms use "blinders" on their pheasants to prevent them from pecking/attacking one another. Blinders are attached to the beak of the pheasant through the "nostrils" (not sure if that's the proper technical term). You can look them up on google. Pen-reared birds raised with blinders will therefore have larger "nostrils" than wild birds. I'm not sure whether the DWR's suppliers use blinders or not.
Wild birds will typically have much longer tails and are stronger and in better condition than most pen-reared birds. They fly faster and hide much better than the pen-reared birds do. It can be hard to explain the differences just by reading about it online, but with some field experience it isn't very hard to differentiate them.
I'm convinced that there are a lot of wild pheasants at Farmington Bay. I can recall a single day (after the season had closed) where I saw at least 15 - 20. Mostly hens. Most of them are extremely difficult to hunt, though, even with a dog. They'll flush hundreds of yards before you walk up on them and head out into the phrag. You'll probably never find them out in that stuff, and if you do, there probably won't be a shot thanks to the 10+ foot tall vegetation.