Gun shows are a massive loophole in existing background check requirements for purchasing from stores, because sales there are instead classified as private sales.
Not all sales at a gun show are private sales. Specifically those from a FFL (Federal Firearms Licenced Dealer). The federal law when first enacted specifically excluded private transfer for commerce clause reasons.
Even if you’re purchasing from a business at the show.
As mentioned above this is inaccurate. If you buy a firearm from a dealer at a gun show sans background check both you and the dealer have committed a crime.
And private sales aren’t required to run background checks.
This is true of actual private sales on the federal level. But several states have further restrictions requiring them.