Except no. Background checks by FFLs are required. There is no gun show loophole. There is a private sale loophole (which is sometimes exploited at gun shows, but is not exclusive to them). This confusion in terminology is pointing to the wrong problem.
If you want to make effective regulations, then you need to understand what regulations already exist, how guns work, and how loopholes are exploited. Otherwise, you get another AWB that bans a bunch of cosmetic features that really don't matter.