Typically, each state in the US will define what is small game and what is big game.
As a hunter, I tend to divide critters into different categories. Small game to me (not including the birds) means squirrels, rabbits, groundhogs, beaver. Predators are fox, coyote, bobcat, cougar, wolf. Big game are javelina, hog, deer, black bear, elk, moose, caribou and pronghorn. Dangerous game would be the brown/grizzly bear (at least in North America).
I guess small game would be something I would shoot with a blunt or judo. Big game would definitely require the use of a broadhead, but then again, I use broadheads on some small game (beaver and groundhog).