As for what category to put the semi auto AK in, I have no idea... I guess you could call it a "semi auto assault rifle," though the terminology gurus will jump on you and say that's a contradiction in terms, since an assault rifle is by definition full auto capable. I guess to be more correct you would call it a "semi automatic version of an assault rifle design."
The term "battle rifle" doesn't have as much of a hard, fast definition as "assault rifle." It was used to describe military-pattern bolt action rifles back to WWI times, and has also been applied to self loading or select fire rifles like the FAL and M-14. I agree that it generally requires a full-power cartridge. As for what sets it apart from any other type of full-powered rifle, like a hunting rifle, I suppose it would be that a battle rifle is designed to be loaded quickly, whether it is from stripper clips on a bolt action, en-bloc clips in an M-1, or detachable magazines in a more modern battle rifle. So basically a battle rifle is a rifle in a full power cartridge designed for use in combat. Not a category I would put the AK in because of it's intermediate power cartridge.