Most belt knives with 3" or longer blade should be versatile enough for a variety of chores, but a hunter would emphasize a thin, keen point for scalpel-like control and precision, AND robust belly for skinning. This is why the drop pt is the most common or favored design. Hunters don't tend to be much longer than 4" because most users prefer to control or "index" the tip with the index finger (get it?), so the blade shouldn't be much longer than your forefinger on the spine, with your middle finger in the choil to maintain control. Control is important because, as Jeff notes, you don't want to puncture the innards and ruin your meat. Although it's probably not a major issue, for the perfectionist, a "true" hunter may have a stick tang rather than the now nearly-universal full tang (or thick enclosed tang), as back-end handle weight would slightly hinder rather than enhance tip or belly control when choked up on the blade.
While there is a good deal of overlap in knife designs and their purposes, I would think a tactical and a hunter would emphasize different features, even if both are, say, 4" drop pts. The tactical or self-defense knife would likely have a relatively thicker point for stabbing and less pronounced belly for better penetration, possibly a swedge along the spine, and perhaps a thinner edge toward the choil or ricasso for finer utility work (or even serrations, yuck!

). A hunter would reverse the emphasis. My uncle, who taught me how to shoot and hunt, would hone his knife to a nearly hair-splitting thin, aggressive edge along the tip and belly, then leave the back half of the blade a little thicker with a polished edge for splitting kindling, whittling fuzz sticks, and similar chores. Simple carbon steels remain popular in hunters, I think, because wear resistance and toughness in a keen edge are far more important than stain resistance.
Sure, one could probably dress game with a "chopper" or a "tactical," but a hunter is optimized for this kind of delicate work.
Glen