That they’re pretty much the same thing but one is considered a pistol and one a rifle. Slightly shorter barrel and no sights make it a pistol?
There was a pretty good explanation up thread.
Short 20,000 ft explanation:
To be legally a rifle the barrel must be 16”. There are also overall length requirements and a few other nits that if they arent applied, you can put yourself into some special NFA (National Firearms Act) catagory. But basically its the barrel length.
One NFA option is the Short Barrel Rifle (SBR). An SBR can have a barrel less than 16”, but you have to get a Federal Stamp and approval for it. Costs an extra $200 for the stamp, and the cost of the extra finger printing and federal background check. But unless your state makes it illegal, like CA, you can get or build an SBR just by being registered and paying the $200 tax.
The AR pistol came about basically to skirt the tax stamp requirement of the SBR. This is why its always been a slippery thing for ATF as the intent of the law is to keep criminals from having a rifle they can hide under a coat or jacket. So you remove the stock of what would have been an SBR, and claim its a pistol that will be fired from the hand without the ability to shoulder.
Practically, as a pistol its very difficult to control accuracy due to weight and not having a shoulder to assist with recoil control, as one with have with a rifle. So to get around that little issue manufacturers came up with the arm brace. Used as designed, your forearm is now strapped to the gun to absorb recoil. It still is impractical for aiming with the brace. More of a shoot from the hip design. But shooters and brace manufacturers have made the braces so that without much effort, it can be shouldered, it just has the brace instead of a stock. Voila, you have in practical terms, an unlicensed SBR.
If anyone ever gets far enough into a legal battle with ATF, its possible they could make arguments that this whole SBR section of the NFA is not really enforceable anymore with the brace approved AR pistol, much less the constitutional argument. Thats why the ATF cant make any clear rulings on the brace thing.