The term "commercial sale" apparently has a specific meaning for purposes of the Manchin-Toomey provision. That is, it's a gun sale by a non-licensee (non-FFL) that involves public advertising (such as being listed on the Internet or exhibited for sale at a gun show). A "non-commercial sale" would presumably not involve public advertising, such as a transaction between family members or friends, and this would be exempted from the background check requirement.
If these "commercial sales" were done as a regular course of business, the sellers would still need to get FFLs. So the Manchin-Toomey proposal only really applies to people making occasional sales in public venues, such as at gun shows or online. How big a part of the market this is, is an open question.