You are stupendously wrong.
"Assault weapon" is a term that was made up by the legislature, and is, very generally, a semi automatic firearm capable of accepting "high capacity magazines", with two or more (or was it more than two...) features from a list of: barrel shroud, bayonet mount, pistol grip, collapsing stock, etc. Cosmetic features. "Assault weapon" is a bullshit term, but it DOES mean something now, since several states have defined them, and the federal government did as well.. "Assault rifle", however, was a term coined in the military to refer to small caliber fully automatic rifles.
An AR-15 of certain configurations is considered, legally, an "assault weapon" by several states and under the previous "Assault Weapons Ban". However, identically functioning and almost identically appearing AR-15's are not. "Assault weapon" is a buzzword made up by the anti-gun legislators because it puts fear into people. I even wanted to ban them before I actually got into the politics of firearms and understood what they were actually talking about. You do not need a Class 3 for an "assault weapon".
An AR-15 is NOT an assault rifle. It is not fully automatic. Legitimate assault rifles (A term no one uses correctly, and a term that really has no use anyway) require a Class 3 stamp because they are fully automatic, and you can't purchase one that was manufactured after 1986, so the few that are out there are $20,000+ guns. But that's ok because poor people commit all the crime, so goes the anti-gun logic.
You are way wrong on the machine gun. NO fully automatic firearms may be purchased by a civilian that were made after 1986. Period. No amount of paperwork fixes that. The class 3 stamp for full auto machine guns is necessary to purchase a pre-1986 machine gun. You can not purchase one made after 1986 (short of some weird stuff with being an FFL "sample dealer" or whatever)
The important thing since all of this is so complicated... Is that Columbine happened during the federal assault weapon and standard capacity magazine ban, and Connecticut still has an assault weapons ban. There was no detectable drop in violent or gun crime when the federal ban was put in place, and when it expired, violent crime has ever since been on the drop. Gun control has been tried. It does not work in the United States.