Only an FFL can ship handguns through the mail, rifles and shotguns anyone can. It even states in the postal regs that postal employees are not to interpret the ATF regs, if presented with a rifle or shotgun they must accept and ship it, legality of recipient and shipper to do so are not their area of expertise. In state transfers are just like face to face, no FFL needed on either end. Out of state, receiver has to be an FFL. If an FFL ships a handgun, he has a form to fill out. Joe Sixpack ships a Mosin, nothing required except postage $$$.
Went through all this with my locol PO, took an email complaint to the district supervisor before "everyone at both your branches has been schooled in the regs now, you should have no further problems shipping in the future". of course, three weeks later I got the same "you can't mail a gun" speech from the satellite branch until they called the main office downtown and they told her the procedures. It seems most have the actual reg printed out in the "book of no-nos" they keep behind the counter and it starts out with only an FFL can ship guns, a paragraph or so below it lists the exception for long guns. They read to "must have FFL to ship" and quit reading.