Sorry, I am just now noticing this.
By the way "FTF" means "face to face" (as opposed to having a gun shipped from buyer to seller).
The short answer is that you are not under the same obligation as an FFL dealer.
They have the ability to (and they must) run a background check on the buyer and verify his identity.
When you sell a gun (any kind of gun) in the parking lot of Burger King you are not under a legal obligation to do any checking on the buyer.
You don't have to because there is no law saying that you must.
If he's a convicted felon, he's committing a crime---but you aren't, unless you have reason to believe that he is a felon.
If he's from out of state and you are selling him a handgun, he's committing a crime---but again, I think you aren't. There is no law requiring it, but asking for the buyers' ID is easy and offers the seller a bit of protection just in case. Some buyers will not do a FTF if the seller insists upon seeing some ID.
(This is what Chicago tries to stop. Chicago gang bangers drive down to Mississippi and buy a truck load of guns off the street then take them back home. Chicago wants to dictate Mississippi law and prohibit it. Too much competition with their Mafia sales I suppose.)
Of course, any of us could be sued in civil court any time for any reason.
I found this and it looks right:
To whom may an unlicensed person transfer firearms under the GCA?
A person may sell a firearm to an unlicensed resident of his State, if he does not know or have reasonable cause to believe the person is prohibited from receiving or possessing firearms under Federal law.
No nonlicensee shall transfer, sell, trade, give, transport, or deliver any firearm to any other nonlicensee, who the transferor knows or has reasonable cause to believe does not reside in the State in which the transferor resides.