I've never heard the term "battle rifle". Probably made up by someone trying to justify calling an AR-15 an assault rifle.
Battle rifle is actually pretty common, as is Assault rifle. Thing is people use the terms incorrectly and make themselves look dumb.
Battle Rifle= Semi/Full auto rifle shooting a full powered round (7.62x51/.308 etc)
Assault Rifle = Select fire (Can do both semi and full (or burst ) ) rifle that fires an intermediate cartridge (7.62x39, .556, 5.45x39 etc)
An AR-15 is not an assault rifle, it's just a clone of the M16/M4 on the outside with changes to make it semi auto only.