you can ONLY 3 whitetail deer, or ONLY 2 bears, etc. Even more serious games tell you what species you can shoot, i.e. For example, you are allowed to shoot three bucks of any species. Ok as for what you do with the shot animals in other hunting games: The way this is done in 'serious' hunting games is that you have a so-called bag limit.
ETA means Estimated Time of Arrival/Achievement.