Years ago, when Congress put a $200 transfer tax on machine guns and silencers, they also put that tax on short-barreled rifles. A short-barreled rifle has a barrel less than 16 inches according to law, which was a fairly easy thing to understand. The problem is, people enjoy finding ways to get around laws.
Back when they passed the National Firearms Act, the idea was that a short-barreled rifle was more accurate than a pistol – and factories even produced stocks for pistols. You could own one of the stocks legally, you could own one of the pistols legally – but put the two together and it was an instant felony. Not a significant problem in olden times – but the AR-15 really created a spot that legislation from the thirties and sixties didn’t anticipate.
The AR-15 has a pistol grip. So if you take a new receiver, you can put on a short barrel (under 16 inches), never put on a stock, and you have a pistol. The military M-4 barrel is 14 ½ inches long. So long as you never put a stock on, you have a poorly balanced, heavy pistol. But it was legal, despite the other drawbacks – which included a buffer tube that kind of extends the frame back about five or six inches.
On one hand, the beastly balance of that AR-15 pistol didn’t enhance one-handed marksmanship. On the other hand, that extra half-foot of buffer tube gave some enterprising shooter something to press against his cheek. Then the next step was a pistol brace that would attach to the buffer tube (where the stock wasn’t). Once the ATF ruled that you could occasionally shoulder a braced pistol, the waters got murky – and by the numbers I’ve seen, there may be as many as 30 million AR pistols with braces in the US – basically one for every eleven Americans. ATF says at least 3 million. I don’t stand behind either number, but either one is fairly large.
Shooters in Dayton (Ohio) and Boulder (Colorado) used AR pistols with braces in their attacks – giving a reason to more precisely define the difference between a short-barreled rifle and a braced pistol. This form seems to be the simplest answer to what DOJ proposes (taken from https://www.guns.com/news/2021/06/07/biden-doj-lists-71-page-proposed-rule-on-pistol-braces )