Ruffed grouse are native to NH, and they have been called Partridge by locals since I can remember, my dad used the term interchaneably when he took me hunting as a kid for them. Back then there were a shit ton of grouse around here before coyotes came in, and houses took all their old habitat. Now your lucky to flush a few a year. They are much more prevalent and huntable in Northern Maine, NH or VT.....if up further north, like near the Canada border you can get into spruce grouse, which have litterally no fear and have to be kicked to fly. Dogs are generally not needed in the far north and you can shoot grouse/partridge with a .22 walking logging roads. Or while deer hunting take the head off them with a .308 or 30/30 like I did way back in the day.
Hungarian Partridge (Huns) and Chukar Partridge are not native to the area and mostly on stocked and hunted on preserves. Much less likely to see one in a "wild" setting.
Pheasants are also non native....to America actually and are Chinese Birds if I recall. They usually cannot survive coyotes, foxes and Northeast winters but are stocked so heavily by some states there are always a few left overs. Pheasants thrive in the midwest because they have shelterbelts of CRP that help them in the winter, and obviously bounties of corn/wheat and grasses from the farm fields, but those were also introduced birds long ago. Hunters in the midwest also mainly shoot roosters so the population stays in good shape, as they practice good management, to keep hunters coming and spending money in their economy.
My bud is in South Dakota right now having a great time hunting pheasants they are getting a good limit of roosters every day. No hens allowed, or if there are they aren't shooting them.