Here in NJ, BB guns are regulated as firearms. So any transfer of a BB gun would require the same requirements as transferring a firearm.
A few years ago, a mayor here in NJ got arrested for shooting at tin cans in his back yard with a BB gun--for unlawful discharge of a firearm.
When paintball guns initially came out, they were also treated as firearms, until a court case changed that--the state attorney general could not justify the classification of paintball guns as firearms due to the lack of clear language in the law. Now paintball guns are simply toys (but can only be sold to 18 and over).