The major variation between military and hunting rounds is "Full metal jacket", military rounds are fully copper clad to make them light armor piercing, which makes the bullet far harder than "soft" lead rounds. Result is threefold:
Bullet is harder, so the rifling in the barrell is finer, giving less rotation, and less long range accuracy. (Military rounds can damage civilian rifling.)
Finer rifling/harder bullet makes for a less "Tight" bullet fit in the barrel, making for a less efficiant holdback of outgassing, less V.
Harder bullet will penetrate armor better, but mushrooms less, resulting in more "clean" through-and-through hits and less of a little-hole-in-big-hole-out result. (This is probably the major reason for the differences in inflicted wounds discussed above.)
Major variation between the 5.56 and 7.62 rounds in terms of utility complaints I've heard is "soft cover". . .the 5.56 will tumble and deviate after hitting foliage and the like, while the 7.62 usually ignores soft cover and remains accurate. (Making the latter round better for punching through jungle or forest soft cover.)
Most hunting rifles and rounds come in "Magnum" versions ALA .306 Magnum. . .which is more propellent. They're almost always soft lead shot, often hollow or scoop point rounds.
Standard sniper rifle is 7.62mm, there are heavier .50 cal ones like the Barrett, or even 20mm ones like the Storm Gun. (Single shot rifles go up to a scale intended for killing elephants with single shots, or conversely punching holes into Armored Personel Carriers or Military Helicopter armor.)
Those .50 cal and 20mm rounds are longer than your hand, especially in the crew mounted m-gun versions.
I forget the citation, but a .50 machinegun round specification retains lethal velocity after passing through "one course of bricks", which is about what your standard post 19th century brick building is made out of.. . .(as in, "No, that one layer brick wall is concealment, not cover.")
