Ahhh, let's see - here in upstate NY, we have the gray squirrel, the black squirrel ( a migrant down from Canada), the red squirrel - which is smaller than either the gray or black and usually lives in the ground- and is often referred to as a ground squirrel, and the chipmunk. Also have Rocky the Flying Squirrel but without the pilot's helmet.
We have woodchucks/gophers but I think they differ from marmots.
Most often we just refer to them as either 'tree rats' or 'rock huggers' - there is a season on some of them so hunting them is not a year round exercise.
I may have left something out, too. Mikey.