What vaccination proof do pet-friendly places actually ask for?

Planning several trips this year and I keep seeing "valid vaccination required" on listings. What do places actually check in practice?

Is my vet's record booklet (with the rabies and 7-in-1 stamps) enough, or do I need a formal certificate? Hotels and resorts seem to say different things from parks and day cafes. Mochi (my cat) is fully vaccinated but I want to know what to carry.