Technically an assault rifle, is semi automatic rifle that also has the capacity to select for full auto fire as well, they are in most circumstances only available to the military. The media has a habit of calling even the semi auto only ones assault rifles, either through ignorance or because it sensationalises the story. They both look very similar(almost identical sometimes) but perform different functions.
Even in countries where semi auto rifles are heavily restricted they are the weapon of choice for pest reduction, animal management, due to magazine capacity and speed of follow up fire
Where ever its legal you can hunt game with whatever high capacity magazine, semi autos you want.
Arguments against hunting with a semi auto, you’ll be carrying more weight due to the high capacity 20-30 rounds magazine(though you can get 5 or 10 round mags).
Under most hunting circumstances for deer sized game or larger you probably won’t be firing too many shots, as even one shot can scatter a herd of animals, or alert other animals in the general area that they are in danger.
Semi autos like AR 15’s are good multipurpose rifles, in that you can use them for hunting, target shooting , or defense.
They seem to be the weapon of choice for mass shootings. However when it comes to military rifles, I would rather be shot with a .223 Ar15 bullet, than a 308, or 30-06 from a bolt action rifle. Vietnam War experience was you stayed down from a body shot from a 308 Cal. A person hit with a .223 could go on fighting and maybe even kill you, unless it was a clean shot to the head.