The army doesn't call the M16 an assault rifle ...
The Army also doesn't call a truck a truck (except for the ones on the flagpole) and they don't call a bathroom a bathroom.
The ATF calls the M16 a machinegun, not a rifle, assault or otherwise.
Combat rifle, battle rifle, assualt rifle, sniper rifle are all somewhat nebulous terms, which, while they have generally accepted definitions in the shooting community, also have extremely broad definitions when used by anyone else.
Again, it goes back to some people defining an object by what it is (a set of physical features) and some defining it by how it is used (sniping, assault, etc.,).
Between the late 1940s and the late 1980s we had a fairly consistant defintion of assault rifle, based on the features of the weapons. And while lots of us, including gun writers often used the term loosely to include semi auto versions of true assault rifles in casual conversation, the way we use "motor" and "engine" in our cars, when it came to tech discussions, we all knew what we were talking about, and what we weren't.
Then came the mass shootings in the late 80s (with semi auto AKs, mostly) and the "assault rifle" hysteria whipped up by the anti gunners and the media.
Most shooters are somewhat technically minded, and prize accuracy. We made a PR mistake when we tried to (accurately) explain that the guns being used in these shootings were not "assault rifles". We were right, but to the press and the general public, if it looks like it, it is, so they kept calling them assault rifles.
We kept telling them they were wrong, and they adopted the term "semiautomatic assault rifle". That lasted for a little while, but it is a mouthful, and not a good sound byte. SO, they created the term "assault weapon". And they defined it. They defined it (in law) as semiautomatic arms with combinations of certain features, and gave us a list of the "bad" features.
Many people today use the terms interchangablely, and incorrectly, still.