Riv-Nut and Nut-sert are brand names. I have a Blue Point "Nut-sert" set whose tool operates more or less like the home-made nut-and-washer setup Rev. Den is trying to describe - that is, it works by rotating a screw in the insert rather than pulling up by leverage as a rivet tool does. Each of the several sizes has a screw-and-nut set that fits into the tool handle. I also have a riv-nut tool that works like a riveter, but it is size-specific, and less versatile.
I also have a box of small Riv-Nuts (branded) , and
as far as I can see there is no functional difference between what is branded as a "nut-sert" and a "riv-nut," and the same tool works for either. Either one will expand wherever it can - i.e. if it's in sheet metal it will expand behind it, and if it's in thick metal it will expand within it.
The Nut-sert set, by the way, came originally from Snap-On..