Certain kinds of firearms are required to be registered, like machine guns, short barrel rifles, and short barrel shotguns.

Tons of guns are not those limited categories, so they are not required to be registered.

Its entirely possible to sell a gun in the US without any kind of paperwork depending on the type of firearm sold, the buyer of the firearm, and the seller of the firearm. I'm in Texas, so I'll use that as an example. Lets say I want to sell a regular shotgun I currently own to a friend. IANAL, this is not legal advice, but my understanding from reading the applicable laws would be all I have to do is verify they are over the age of 18 and that I think they are probably legally able to own a gun (I have no prior knowledge of any legal restrictions against them owning the gun). We can meet up, check he's probably over 18 and can probably legally own a gun and is a Texas resident, he can hand me cash or whatever for trade, I can give him the gun, and we go our separate ways. I do not need to do a background check. I do not need to file any registration. Nobody would know this guy now owns this gun. I do not need to keep any record of this sale at all. This shotgun has been an unregistered gun for its entire exstence.

This wouldn't necessarily be true if I trade some certain amount of guns as then I would probably need a federal firearms license and thus have some additional restrictions on facilitiating a sale. This also isn't necessarily true in other states which have additional restrictions on gun sales. But if I haven't done any gun sales in a long while, such restrictions wouldn't apply (according to my current understanding of the law, IANAL, not legal advice).