Gun laws are even more stupid. Allow me to demonstrate with some visual aids.

[1] - What you have here is an AR-15 rifle. The serial number on that receiver is registered as a rifle. This is a legal weapon.

[2] - This is an AR-15 handgun. It fires the exact same cartridge as the one above, but the serial number on this receiver is registered as a handgun. This is a legal weapon.

[3] - This is an AR-15 rifle. 'This looks exactly like #2!' you say. You're correct. It's utterly identical to #2. However, when it was made, this receiver was registered as a rifle, not a handgun, and thus in the eyes of the ATF it will always be a rifle. If the receiver were registered as a handgun both #1 and #2 could be made of the same receiver (converting a handgun to a rifle) and be legal, you cannot do the opposite, and make a rifle into a handgun. Since this weapon is a rifle turned into a handgun, it is considered a 'short barreled rifle', and is subject to more legal constraints than ownership of pyrotechnics and nuclear material are.

[4] - This is an AR-15 rifle. Notice the similarities between #1 and #2. It is irrelevant whether this receiver is registered as a rifle or a handgun, this weapon is illegal as detailed above. Why? Because it has a buttstock on it. If it's registered as a handgun, putting a buttstock on it makes it a 'short-barreled rifle'. If it's a rifle, cutting the barrel makes it a 'short-barreled rifle'. Despite the fact that this weapon is exactly as deadly as the previous examples, and more difficult to conceal than the handgun variant, it is more illegal to own this weapon without jumping through a circus of legal hoops than it is to possess child pornography.

[5] - This is an AR-15 handgun. 'Now you're just fucking with me' you say. I'm not. Since this is a handgun, it is illegal to take a rifle (#1) and convert it to this. However, if it's a registered handgun to begin with, this is now legal, because that stock is not actually a stock, it's an arm brace. Thus, this is a perfectly legal thing to own.