You correct. The semi-auto AR-15 is not an assault rifle, but it was and is an “assault weapon” as defined by the expired Federal AWB and several states’ current laws. A lot of people think the AR is short for Assault Rifle when in fact the AR stands for Armalite, the original manufacturer.
The old Fed AWB (modeled on the California ban which preceded it)defines an assault weapon as a semi-auto firearm that uses a detachable magazine and has more than one of the listed features: Pistol grip, flash hider, collapsing, folding or detachable stock, bayonet lug, or a barrel shroud.
You can bet the next Fed AWB ban will not allow any of the listed features (particularly the evil pistol grip) on any long gun.