The labels on these things end up being one of the core problems. What is an assault rifle? What is a high-cap magazine? Certainly these terms are familiar to those of us with experience with firearms. But to hear politicians throw the terms around, you'd think they had no clue (and I suppose they often don't), even though they supposedly have "experts" on hand to help them make their decisions. What it (usually) boils down to is people with a decision already made going into the "decision-making process" and justifying their already-made decision with whatever materials and personnel they have on hand.
Which is the wrong way to run anything, let alone a government.
The legalities of what kind of rifle you're allowed to use to hunt what where and when and the particular ammo and how big of magazine can be used are somewhat arbitrary and vary from state to state and game animal to game animal. I think at least 48 at states allow some form of hunting with semiautomatic rifles.
In some parts of the country "Bubba'd" SKS guns are pretty popular for hunting deer I think. (Google image search "bubba gun sks" for a general idea of what's going on - converting a wood stock and 10-round stripper clip magazine to polymer with detachable box magazines, which is a pretty good illustration of how the same gun can look a lot different.)
Actually it's the other way 'round - the AR-15 came first; the M16 is based on it. Also, detachable magazines are often cited as another requirement for classifying a rifle as an assault rifle.
The main difference between an AR-15 and a hunting rifle is that the hunting rifle tends to use a more powerful cartridge. The rest is cosmetic.