Trying to figure out what exactly they are passing doesn't mean I'll comply with it ...
The National Firearms Act was passed in 1934, and has been amended several times over the years.
If put all firearms in classes, rifles, shotguns, pistols, machine guns, my favorite "any other weapon", and destructive devices. The statute defined and regulated each type of firearm to some degree, i.e. rifles had to have a certain length, shotguns had to have a certain length, pistols couldn't be smooth bore, destructive devices had all sorts of rules, machine gun was defined, and so on.
For the purposes of this discussion, the relevant LAW is on the definition of "rifle", which is, in part, "The term “rifle” means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder" Then the law goes on to define firearms made from rifles by their overall length and barrel length.
The law is pretty basic and does not have much elaboration.
The sand in the gears is what does "designed", "redesigned" "intended" mean in the statute, because they are not otherwise defined.
This is where the rulemaking power of BATF comes in. Most federal laws since about the beginning of the 20 century have a broad outline of the law, and then refer the details to a federal bureaucracy which has great leeway in defining terms and filling in the blanks. (There is a case on this matter before the Supreme Court right now).
BATF (and any other agencies) can promulgate any rule it wants that it contends is consistent with, and necessary for enabling a statute enacted by Congress. Congress has basically abdicated its responsibility in this area, letting lifelong bureaucrats actually make most of the law the effects our daily lives.
The agency has to use yet another set of laws to publish a draft of a proposed rule, allow for public comment, kick it around, and then make a decision on whether to implement the proposed change, modify it, or forget about it. the agency is bound by this Administrative Procedures Act for the formalities, and by a considerable body of law on what standards the agency has to use to enact a change in the existing RULES.
It is going to be up to BATF to define (or redefine) what does "intended" mean, what does "designed" mean? All sorts of things are used for purposes for which they were not designed or intended to be used, so those definitions don't just jump out at you.
For all practical purposes, Congress is not part of this discussion.
One of the big hurdles BATF is going to have in redefining "braces" as "stocks" is one of the things the courts look at in deciding whether an agency is being arbitrary (in the legal sense) is the prior practice and rules of the agency. In this case BATF has examined any number of braces, and issued letters of acquiescence to the manufacturers, and so it will have to come up with a reason why IT could not have, or did not determine that braces violated a 1934 law. In other words, what has changed that makes the proposed changed desirable?
I suspect we will see regulations that more clearly define what is a brace and what is a stock and nothing will be "banned". Some manufacturers will have to move to plan B.
The final thing to remember is that regulatory change typically is not very swift. If can take years for the agency to work through the administrative process.