In L.E.O. community they are normally referred to as “Patrol Rifles” Most commonly an AR variant, usually semi-auto, but could be oddballs like an SKS (usually a budgetary choice)or an M1 Carbine. Is occasionally an AK type.
The term is always duty rifle, duty gun, patrol rifle or gun, or by name such as AR, AR-15 , HK, MP5, FAL, FN, or just plan gun, rifle or shotgun