A "Counter Assault" rifle is a select fire rifle in an intermediate caliber. AK, M16, Galil etc.... I cant remember the general that came up with the term but it is just anecdotal.
This is opposed to a Main Battle Rifle or battle rifle that is a term developed after WW2 that is used to describe a rifle that is fed ammunition via a detachable magazine and fire a full-powered rifle cartridge Such as the M14 G3 and FAL. This term may also describe earlier full powered semi automatic rifles such as the M1 Garand, Gewehr 43and SVT-40.
https://en.wikipedia.org/wiki/Battle_rifle
Firearms that are fielded by militaries can be described under the blanket term Service Rifles.