State laws vary widely. In CO, I can sell a handgun to a resident with zero paperwork, which I recently did. I can sell a longgun to anyone
, although I would require a bos with them stating they are legally allowed to possess a firearm. With the handgun, I still had him sign the bos and state he was a CO resident. NH is about the same, but other states may be more complicated. Easy enough to look up state law. Out of state, "interstate" sale has to go thru a FFL at the buyer's home state, not the seller's.
The Federal Firearms Act barred interstate sales between nonprohibited persons only when the buyer's state required, and the buyer lacked, a license to purchase. S. 1-90 drew a line between "long arms" (shotguns and rifles) and other firearms (primarily handguns). Persons who were not licensed dealers could purchase handguns only in their state of residence. Residents of different states could sell each other rifles and shotguns so long as the receipt did not violate state or local law at the buyer's place of residence. Dealer "mail order sales" of any firearms were barred by a provision barring a licensee from shipping firearms or ammunition to a nonlicensee in interstate commerce.
I am not sure where you got your quoted information above, however, in you post, the first bolded part is absolutely not true, according to Federal law, which trumps all states' laws. The second part bolded applies universally to handguns, but not necessarily to all longgun sales. The applicable parts of Title 18, Chapter 44, Section 922 of United States Code is posted below.
Sec. 922. Unlawful acts (a) It shall be unlawful-- (5) for any person (other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector) to transfer, sell, trade, give, transport, or deliver any firearm to any person (other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector) who the transferor knows or has reasonable cause to believe does not reside in (or if the person is a corporation or other business entity, does not maintain a place of business in) the State in which the transferor resides; except that this paragraph shall not apply to (A) the transfer, transportation, or delivery of a firearm made to carry out a bequest of a firearm to, or an acquisition by intestate succession of a firearm by, a person who is permitted to acquire or possess a firearm under the laws of the State of his residence, and (B) the loan or rental of a firearm to any person for temporary use for lawful sporting purposes;