While they are all small arms, the most common ones, the military version that is, are called "assault rifles", which are defined as a select fire (either full auto or burst fire) rifles firing an intermediate power cartridge. Examples are M16/M4, AK family, SA-80. Some "Assault Weapons" aren't even rifles, but rather pistols or shotguns. Others are full power semiautomatic rifles, or pistol caliber semiautomatic carbines, some of which are submachine guns in their full auto versions. Some are more or less ordinary pistols
I was an officer in the Army in the 1972 timeframe. Nothing was called an "assault weapon" while I was there. There were "small arms" (select fire or single fire), "anti-tank", "grenade launchers", and "crew served" weapons. I never heard "assault weapon" uttered by a single person in the military.