No after the second visit they received a “card” which, in typical government fashion, has excess detail info crammed on both sides. Plus in Florida only certain companies or orgs. have the vaccines so if an individual doesn’t have the card from one of them then red flags for the communists at the airport.
Yeah I got that card here in Indiana when I got the Moderna vax.
But any of my middle school grandkids could duplicate that card in about 10 minutes.