I've always been curious... at what point, if any, does it just become a pistol? If (just for the sake of argument) I take a single barrel break action .410 and cut the barrel to 5 or 6 inches and cut the stock off so that just enough to grip it is left, would that be considered a pistol?
In your scenario no, you're making a short barrel shotgun or AOW which is a $200 tax stamp on a BATFE form 1. It was originally manufactured as a shotgun, that's what it is for the lifetime of the firearm.
You can go from pistol to rifle without issue, you cannot do the reverse if the given serial number was ever
recorded on a 4473 as a rifle or shotgun.
If it has ever
had a shoulder stock on it and has been recorded on a 4473 as a rifle or a shotgun then you have to get a stamped BATFE form 1 to make it into a pistol as technically you'd be making a short barrel shotgun or any other weapon out of a shotgun.
It becomes a pistol in the eyes of BATFE if it was transferred to you as a other firearm (stripped receiver or frame) or a pistol and has never
been transferred as a rifle or shotgun and you build a firearm out of it that only has a pistol grip.
This is why if you build AR-15s or AK pistols you have to make sure the virgin receiver has been transferred to you as a pistol on the previous version of the 4473 or other (stripped receiver) for the current version if you intend to make a pistol out of it.
BATFE's stand on firearms is this, it is what it is after it has been transferred on a 4473 or what it is originally manufactured as. You cannot go back without going through the hoops of getting tax stamps except going from pistol to rifle. You also can't take a rifle that's been transferred to you as such on a 4473 then remove the stock and put a short barrel on it to make a pistol. It came from the manufacturer or FFL as a rifle, that's what it is for the lifetime of the firearm.
You also have to be careful when converting an AR-15 pistol into a rifle. You have to put the long barrel on it first before
the shoulder stock. Do it the reverse and that receiver is not on a stamped BATFE form 1 or 4, get caught and you have an unregistered short barreled rifle which is up to a decade in camp fed and effectively a permanent loss of your RKBA.
Shotguns are a special case because they are not handguns because of the bore size except for .410 GA. Shotguns are either short barreled or AOWs (any other weapon). I cannot legally possess a short barrel for my Remington 870s in my home until I have a Remington 870 receiver that's on a BATFE form 1 since I have a pair of Remington 870s in my home. Having the parts to make a short barrel rifle/shotgun or a machine gun falls under "constructive possession" and is just as bad as actually possessing the unregistered NFA item. I can have short AR-15 barrels in my home now because I have six virgin AR-15 receivers that are not a pistol or a rifle yet. Since I could be making pistols with those AR-15 receivers, I'm not doing anything illegal by having short AR-15 barrrels in my home. If I had short AR-15 barrels in my home prior to taking possession of my six AR-15 receivers last Thursday I would be in violation of NFA because I have a complete AR-15 in my home that was manufactured as a rifle the only thing I could possibly make with those barrels with the parts on hand is a short barrel rifle so I could have gotten nailed for constructive possession of an unregistered short barrel rifle.
To be 110% legal without any ambiguities if you intend to have firearms that can be easily converted from non-NFA to their NFA short barrel counterparts you should have it on a stamped BATFE form 1 or 4 that way if you do make a mistake and put a short barrel on it before removing the stock it's already legal.
This is also important if you've come across with three hole AK receivers that have a rivet through the hole for the auto sear. BATFE's stand on that is once a machine gun, always a machine gun. If you see one of those early MAK-90 variants don't handle it, just look at it and walk away fast.
This also applies to machine gun parts. I have a complete AR-15 and six stripped lower receivers. I cannot legally possess any M-16 parts in my home unless I have a RDIAS (registered drop in auto sear) or registered lightning link. Those individual registered serialized parts is the actual machine gun. I can have any number of AR-15s with M-16 parts as host firearms to use the RDIAS or registered lightning link in as I'd need an AR-15 with M-16 parts to use it.
I hope I made it clear. When dealing with NFA items you need to understand the legalese of what you can and cannot do and what is construed by BATFE as 'constructive possession."