*Boomer, you beat me to it*
Well you can have standard hunting rifle, dedicated target rifles and you can go in between. Standard hunting rifles generally have lighter contour barrels. If your going to be carrying a rifle all day, you don't want too much weight. In most instances, you can get hunting rifles in very powerful cartridges capable of handling all of the worlds most dangerous species, or very light cartridges for the smallest game. The powerful rifles develop tremendous recoil, and the little guns develop hardly any by comparison.
Target rifles can come in darn near any cartridge you want, but your probably not going to find many elephant rifles at any matches your likely to attend. Generally each rifle itself is speciallized for a particular style of shooting. Some have wide forestocks for resting on bagged rests, some have special grips and stocks for firing offhand, and some look like they belong in a star wars movie.
If you go in between, you can buy yourself heavy barreled rifles that many call "Varmint" or "Tactical" rifles. It really depends on who's buying the rifle to call it whichever they want. They look so much alike that most can be called either, with a few exceptions. With these rifles, (And I'm just going to assume this is what your thinking of) you'll usually find heavy barrels with somewhat beefier or more speciallized stocks. The heavy barrel does a few things, but again it depends who you ask. First, the added weight will help to absorb recoil allowing you to stay on target easier. It also helps hold the rifle steadier, and soaks up heat from firing better than a light barrel. It's also more rigid. As you fire a bullet, and it travels down the bore, the barrel actually oscilates in a circle as the bullet spins with the rifling. As long as the barrel stops in the same spot each time the bullet leaves the barrel, there's no problem. Acuaracy will be repeatable. If it doesn't, you'll have troubles. Heavy barrels flex less, and that will keep the oscilations under control.
While you certainly could hunt with a dedicated target rifle, most wouldn't want to. And in my opinion, unless you don't have to walk too far, you probably don't want to hunt with a heavy barreled rifle, either. It may not feel like much in the Morning, but after carrying a rifle all day, walking uphill both ways and through ten feet of snow, at the end of the day that rifle will feel like a refridgerator. Good luck with your purchase.