There's no generally accepted definition that holistically defines a hunting rifle, but logically a hunting rifle is one that is designed for the purposes of hunting. The design features can vary significantly depending on the kind of game the hunting firearm is designed for use with. Twenty-twos and similar firearms would be suitable for very small game, and then a centre-fire cartridge for hunting big game, for example, in a rifle that supports that. Shotguns are generally used for hunting birds, although they can be used for big game hunting as well.
Tactical firearms, on the other hand, are firearms that are again, broadly speaking—there's no accurate, holistic definition of what is a tactical firearm—associated with military and police.