You must be able to prove that you have been fully vaccinated (plus 14 days) with a document (digital or paper-based) from a national or state-level public health body that includes, as a minimum:
forename and surname(s)
date of birth
vaccine brand and manufacturer
date of vaccination for every dose
country or territory of vaccination and/or certificate issuer
If your document from a public health body does not include all of these, you must follow the non-vaccinated rules. If not, you may be denied boarding.