yeah, in order to be an assault rifle it needs all of the features of a civilian version (self loading, detachable box magazine, intermediate cartridge) but it also needs to be select fire (safe, semi/burst, full auto)
a battle rifle is basically the same except for firing a larger cartridge (think FN FAL, HK G3, M14)
these are terms that had meaning way before becoming politicized and misused. bothers me to no end. don't even ask me about clips.