That said, though, I find the distinction between "assault" and "regular" rifles to be quite silly. In practice, "assault" tends to mean "it has a rail for attachments and looks scary", just like "sniper rifle" tends to mean "rifle with a scope". In both cases, the essential portion of the definition is does not have anything to do with the gun, but more to do with the person carrying it. A sniper rifle is a rifle carried by a sniper. Even a relatively weak .22LR can be a sniper rifle in sufficiently skilled hands. Similarly, an assault rifle is a rifle carried by someone with assault training.
Anyways, none of this impacts the fact that the term "assault rifle", as introduced with the German Sturmgewehrs and now subverted by the U.S. media to mean "scary looking gun", has a specific military meaning that distinguishes it from other small arms like the battle rifle. Let's use Wikipedia's definition: An assault rifle is a selective fire ... rifle that uses an intermediate cartridge and a detachable magazine.
The distinguishing features of the assault rifle, compared to the contemporary battle rifles at the time it was popularized (like the M1 Garand), is that it is chambered for a lower powered non-pistol cartridge (which translates into lighter weight), has a detachable magazine and is capable of burst or fully automatic fire.
I'm not aware of any military or paramilitary organization that uses a definition substantially different from this, or anything like the one you've suggested.
Drawing a line between civilian and military use suitability is difficult, but that doesn't mean there is no difference. That's why there is no assault rifle law in the US, but rather some features of weapons have been banned from private use.
A few states do outlaw or ban some specific NFA weapons however - for instance 5 states outlaw individuals from possesing machine guns.
The gist was that I don't believe the government bothers with banning knife-ads while semi-automatic rifles (under whichever label) are sold freely.