I am no better when it comes to hunting, I will google to see if there is anything in between bird and deer in size.

Edit: Google search found this list
Big game: white-tailed deer, mule deer, moose, elk, caribou, bear, bighorn sheep, pronghorn, boar, javelina, bison
Small game: rabbit, hare, squirrel, opossum, raccoon, porcupine, skunk, ring-tailed cat, armadillo, ruffed grouse
Furbearers: beaver, red fox, mink, pine marten, musk rat, otter, bobcat, coyote
Predators: cougar (mountain lion and panther), wolf, coyote
Upland game bird: grouse, woodcock, chukar, pheasant, quail, dove
Waterfowl: duck, teal, merganser, geese, swan