If a card is sent in to PSA and is graded, if somebody else buys the card and sends it in to be re-graded again by PSA, is the serial number the same???

Reason I ask, is I am watching a card on Ebay. I went to look at what it had sold for in the past and i found the exact same card but went from PR to PR-FR1 and still had the same serial number.

I was just curious if this is indeed the same card or if somebody was running a scam with holders and using the same serial numbers.