Burning a token means removing it from the chain moving forward. All data will exists of the token from the past, including ownership and time of burn, but moving forward no one will be able to own or re-mint it.
The burn button will burn all your currently owned things, so here two NFTs will be burned. You cannot burn when a token is in possession of another, even if you minted it. After you sell or transfer, you cannot burn those NFTs anymore, only the current owner can.