Some laws or proposed laws say a pistol grip and box magazine == "assault rifle". Most gun people would call a rifle that looks like an M-16, AK-47 or FN an assault rifle.
No private citizen can buy a machine gun today.
The dirty secret of the whole gun control thing is that most of the issues associated with people stockpiling weapons and smuggling pistols were dealt with in 1934 via an excise tax.
Basically, any short rifle and some pistols were subject to a $200 tax ($3400 today). Instead of blanket bans, the law defined classes of weapons and taxed them out of the market.