Unless you bill of sale is notorized, it really means nothing. The other person can say "that is not my signature" and you have no way of proving it is.
Correct but if anything goes south later you can see their name and the serial number and address on a paper and give a copy to law enforcement. I had a buddy that sold a gun that was traded for a stolen gun. His paper work cover his backside and made it easier for Leo track down the trash