From my understanding as a general citizen, who owns several firearms but purchased them all from stores, and has done some research but not a lot...
A license is not required for most firearms and many/most states don't require registering firearms at all. Unless you're getting into things that require special federal licenses.
Gun shows are a massive loophole in existing background check requirements for purchasing from stores, because sales there are instead classified as private sales. Even if you're purchasing from a business at the show. And private sales aren't required to run background checks. No expectation for an individual selling a firearm to have to pay to run a check on who they are selling to, so no requirement for private sales.