The US (and because of it a large chunk of the world) has a peculiar idea that the "receiver" is the crucial bit of a gun. That is, the central block that everything else attaches to or screws onto. So the receiver is the part that's regulated, controlled, etc.
The reason this is a peculiar idea is that the "receiver" is usually just a few bits of sheet metal cut, drilled, and bent to shape and then bolted - which somebody could make in an afternoon in a home shop.
So for example someone could get mail-order parts for a barrel, a trigger, a magazine, sights, etc without incurring legal difficulties... but would have to do legal and registration paperwork if they were to try to get a receiver. Until they either buy a receiver, or else fabricate one AND assemble and fire the resulting gun, what they have is not legally a "firearm."
Laws vary from place to place, so don't bet your freedom on this, but as I understand it, as long as you have not obtained a receiver, it is not legally a firearm. Any thing you have created in the shape and form of a receiver does not legally become a receiver, until you actually fire a bullet. And at that point, if you created the receiver in your home shop rather than getting it from someone else, you are the manufacturer of the resulting firearm rather than anyone who manufactured or sold you any of the more difficult-to-fabricate parts.
But there are lots of finicky bits to this law, so don't try funny stuff like buying a firearm outside the US and then importing everything EXCEPT the receiver -- it won't legally work the way you'd hope. And if you live somewhere else, there are bound to be lots of finicky bits to your laws too, which I wouldn't even guess at.
You are right about pretty much all of this, except a receiver legally becomes a gun the moment it is able to be assembled into one, not once it fires a bullet or is assembled. Thats why they sell so called 80% receivers which are mostly complete but need to be milled further to be technically a receiver. It is legal to manufacture your own gun at home as long as you do not sell it, transfer it to another party, or leave the state with it. This is the main reason the government was so freaked out over 3-D printed guns, because they know under current law they can't do much about it. Gun laws are a funny thing, and they consider possession of all the parts needed to make a specific weapon the same as ownership of that weapon.
For example, I own a semiautomatic AK -47 variant. There is a trigger group kit that is sold from many retailers that allows you to turn a semi-automatic AK variant into a fully automatic rifle. The trigger group by itself is legal, but if I own the gun it fits in and simply order the parts, I can be punished the same as if I have a fully automatic weapon without a license, because they see that as intent. Unfortunately the gun laws in the US are purposely made to be confusing and ambiguous so that people fear to even go there.