The ones I have seen are made of card stock and the vaccine lot labels are sticky tape.
People are told “this is your card. This is the only record we currently have that you have had the vaccine. Do not lose your card bring it back for your second round. “
A small fraction of people show up with the card the second time because it was laying by their seat where they sat for 15 minutes and got trashed when they left.
Before making a fake card, I suppose it would be good to take a look at a real one. But I would never make a fake one, because that would be wrong.