I went to a warehouse to replace a damaged MEMBERSHIP card the other day, and they said okay but I had to take a new picture. I said, sure why not, and got a new card on the spot and thought nothing of it. But then just now, I receive a new Costco CREDIT card in the mail claiming that it was a replacement for my lost/damaged CREDIT card

May be this is a standard procedure, but I don't recall this with my previous AMEX card (otherwise they would be sending me a new card every time I moved, for instance) .