Assault Weapon is not a term generally used by gun owners who are pro-2nd Amendment and fairly knowledgeable about firearms in general. It is a term that is used by various groups seeking to ban guns or impose more restrictions on gun ownership, and often the general public that is not very knowledgeable about various types of firearms, and how they actually work.
It's like labeling a Camaro a "race car"; a Remington 700 30-06 a "sniper rifle"; a large kitchen knife an "assault knife"; or a hammer a "mace".
Guns are usually classified by the way they work, like:
Lever-action / repeaters
Semi-automatic
Bolt Action
Select-Fire (full-auto or semi-auto selectable via a switch)
Single Action, Double Action, Double Action Only
Striker fired / Hammer fired
Revolver
And, when you get into shotguns, they have names describing what type based on their barrel configuration and action type.
So, "assault weapon" is really a very politically weighted phrase used by special interest groups determined to heavily restrict and/or ban guns altogether.