They stamp on passport, scan it and scan the PR card from what I could see.
I am sure they allow for the fact that you may have changed your passport. Back when we had the old form folded up inside the passport, it was never a problem because they know years later that you will not have the same passport.
According to
http://www.cic.gc.ca/english/information/faq/pr-card/pr-card-faq10.asp you do not need a PR card if you arrive at the border in a private car.