The named concept of the battle rifle existed after most battle rifles had fallen out of service. As far as I know, the term is seemingly one made up by firearms enthusiasts to describe rifles that fall outside of the realm of an assault rifle, or sniper rifle. In the firearms industry, we like to make shit up, but occasionally something sticks. Battle rifle was something that stuck.
When most people say battle rifles, they are talking about semi-automatic rifles that fire a full-powered cartridge like the 308, 7.62x54R, and even the newer 6.5 Creedmoor would qualify. These rifles can be select-fire, but its not a requirement. As you’d expect, this includes guns like the AR-10, the FN FAL, the G3, the M14/M1A, and the most modern model on the market, the SCAR-H. These rifles define the contemporary battle rifle, even if most are not that modern.