The idea of Class IV (or any other class number) weapons is mostly born out of video games and movies. There are ATF weapons classification types, but few people refer to them in regular conversation. They exist mostly for the purpose of regulating and licensing the import, sale and manufacturing of different kinds of guns and weapons. Of course, some weapons must also be registered with the ATF.
Surprisingly enough, it is possible to own Class IV weapons, as they just require registration and a tax stamp. Collectors of rare and unusual weapons, some types of security contracting firms, manufacturers and people who sell to law enforcement and government all handle and own different kinds of Class IV weapons. Many historical arms from both World Wars would be Class IV weapons, as would many modern devices.