"XYZ Wholesale is selling complete Blastomatic kits, everything but the serial-numbered part, for $189.99. You want I should order a few?"
"Fish around in the bottom of that box from Acme Tactical. There's a couple of serial-numbered parts in there that I need to put in the logbook."Used outside that setting, this can cause confusion. Many firearms have the serial number on several parts (you will hear collectors of old guns refer to an example of a Mauser or Luger or Peacemaker as having "all matching numbers".) There is a reason for this, however.
Regardless of your feelings on gun control laws (and I think they're pretty much all unconstitutional), we have them. If the government is going to have laws that control guns, they have to define something as the "The Gun". In other words, if they are going to have a law saying, for instance, that you can't mail a handgun, then they can't let you just take a handgun apart and mail the complete thing as "gun parts"; there has to be an "atom of gun", a piece that, no matter how many other pieces you remove, retains its "gun-ness", and that is the part that is controlled.
In most cases it's fairly obvious: There is a frame or receiver that all the other parts (lockwork, barrel, cylinder, whatever) bolt up to, and that part is the gun. Several common exceptions to that rule or variations on it can be confusing to the casual hobbyist, and I'll try and cover a few here:
With self-loading rifles, it's usually pretty apparent at a glance. With most designs, the controlled part is the piece that the barrel, bolt and magazine all go into. Two big exceptions are the AR-15 and the FAL, which have "upper" and "lower" receivers. With the FAL, the upper contains the bolt, barrel, and magazine well, and it's obviously the controlled part. The AR, however, has the mag well on the lower receiver. Part of what has made the AR such a hit in the aftermarket is that the whole top half of the gun is unserialized and barrel length, caliber, and dozens of other features can be changed simply by swapping uppers out, since only the lower is controlled. It's really something of a fluke in the rifle world, but thank heavens for it, because it has spawned a whole hobby within a hobby.
With self-loading pistols, the frame is almost always the controlled part. Generally this is easy to tell, because even with most of the rest of the parts taken off, the frame still looks like a gun. Major exceptions would be the Ruger .22 semiautos, in which the barrel and its integral receiver are the gun and the grip frame is not; the Luger, in which the "slide" is the receiver; and the Beretta Neos, which can have its grip, barrel, and bolt all removed or changed out, leaving only the receiver as the actual gun.
In revolvers, confusion can also arise. The frame is, again, the gun, but most old single action revolvers and their modern clones have removable grip frames. The controlled part is the part of the frame that the barrel and cylinder mount to, not the separate "grip frame". Charter Arms double action revolvers are similarly constructed, in that the grip frame is separate from the actual frame of the gun. This sometimes causes confusion on eBay when someone freaks out over seeing a "grip frame" being auctioned.
Bolt-action rifles have a rather obvious receiver. For whatever reason, the Russians numbered their Mosin Nagant rifles on the barrel, rather than the action, and everyone else that made Mosins followed suit. Since these rifles are so rarely re-barreled, it's not that big of a deal. If you ever do, make sure to have your gunsmith move the S/N to the receiver. (Some importers these days are marking the receiver to fix this.) Mausers are generally serial numbered on the receiver as well as having the bolt and bottom metal numbered. If the gun has been re-arsenalled at some time in the past, these numbers may well not match. It should be obvious that the number on the receiver is the one that matters.
This is generally all common sense. I'm no rocket scientist, and I managed to pick most of it up by deductive reasoning. If you can figure out a 1040EZ, you can probably figure out which part of the gun is actually the gun.