Based primarily on the features of the German Sturmgewehr, the commonly accepted definition of "assault rifle" in the military and shooting community was;
Select fire, magazine fed, intermediate power cartridge (based on common WWII standards, more powerful than a handgun round, yet less than the standard infantry rifle round - .30-0-6/8mm Mauser/7.62x54R, etc). Other features common to, but not making the rifle an assault rifle by themselves were (relatively) straight line stock, and pistol grip.
Beginning the late 80s (originating after the 1986 Stockton CA schoolyard shooting rampage) the media and various gun control groups began focusing on weapons of military appearance, particularly the AK 47 (semi auto version) and expanding to cover all "look alike" rifles. They tried calling them "semi-automatic assault rifles", but this proved to be too cumbersome a sound bite.
So they created the term "assault weapon" and used it to refer to rifles, handguns and shotguns with military appearance. By 1994, with the "Assault Weapon Ban" law, they got a definition codified in law. That defintion covered semiautomatic firearms, with certain combinations of cosmetic features, including detatchable magazine, pistol grip, bayonet lug, flash hider/suppressor, and others. Some states copied the 94 AWB, without the sunset clause, and some have even expanded on its definitions.
Note that no actual assault rifles (legally machine guns, and already covered under the 1934 NFA) were affected by the 94 AWB, or any of its state clones.
Indescriminate use of the two terms since those days has left most ordinary folks ignorant of the correct defintions. So most people just repeat what others say. Dictionary references are not a good source for correct defintions of technical details, as they are concerned with the defintions found in common use (and not whether the common useage is correct or not), and clearly say so in the prefaces of most dictionaries.
Translating from a foreign language is ALWAYS open to some interpretation. Sturmgeweher is usually translated as assault rifle. Sturngeschuetz (a turretless armored vehicle) is translated as assault gun. In these cases, the English word assault refers to a military assault, such as assaulting an objective, not the common legal defintion of one person harming/attacking another.
Interestingly, Sturmvoegel (one of the nicknames for the WWII German jet fighter) is usually translated as "Storm Bird", and not "Assault Bird".
Nicht wahr?