the "assault weapon" derives from yet another ww2 german innovation, the SturmGewehr44, literally "assault rifle 1944". an improvement over the earlier bolt action rifles and submachine guns, the STG (initially rejected by Hitler) was full-automatic-capable and had a pistol grip and removable box mag like the sub-guns, but fired an "intermediate" rifle cartridge, hence combining the benefits of range and power with ammo capacity and rate of fire.
i currently own 3 semiautomatic rifles which might or might not fit the definitions.
m1 Garand, blue sky Korean reimport, receiver 1943 by Springfield Armory. 8-rd en-bloc clip in internal magazine. 30-06.
m14(s), Polytech semiauto M14 clone. the receiver and barrel are chinese, but many USGI and aftermarket replacement parts. uses a removable box magazine, .308/7.62x51.
ar15, semiauto clone of m16. bushmaster lower, parts set upper. pistol grip, removable box magazine, .223/5.56x45.
of the three, the M1 has actually been to war in the pacific and korea. not usually considered an "assault weapon" because of the limitation of the internal mag, and lack of pistol grip.
the M14(s) can be considered an "assault weapon" due to the removable box magazine, and the USGI m14 is select-fire. some later variants added a pistol grip.
the AR15, (Armalite Rifle) derived from the m16 is semiauto, often called an assault weapon due to its box mag and pistol grip. the US poster child for "assault weapon", along with the russki AK47.
note that none of these fit the formal definition of "assault rifle" because they are semiauto, but are often loosely and arbitrarily defined as "assault weapons". the defining features of an "assault weapon" appear to be the box mag and pistol grip. other options which further complicate the definition are bayonet lugs (m1, m14(s)), flash hiders, and "bump stocks" which simulate full-auto.
confusing? you betcha.
defining features:
assault rifle(technical definition): full-automatic capable, removable magazine, pistol grip, rifle cartridge.
Assault weapon(legal definition): semi-auto, removable mag, pistol grip, flash hider, bayonet lug.