Do veterinary clinics have compliance requirements like medical offices?

Veterinary practices are generally not HIPAA covered entities, since HIPAA protects human health information. That does not leave you unregulated. You handle payment cards, which brings PCI obligations, and you hold client personal and financial data covered by Florida data breach notification law. Practices offering in-house payment plans or financing may also fall under FTC Safeguards.

The practical version: protect client and payment data properly, and be able to show what you did if something happens.