Cryptography - X.509
About
A x.509 certificate is the specification / version of certificate in the X.509 Public Key Infrastructure (PKI)
It's the most common and used format of a certificate. certificate and X.509 certificate are generally terms that are interchangeable.
This certificate is defined in the rfc5280 - Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile
When you see x509 as the command of a cli, they refers to the X.509 certificate. For instance openssl has a x509 command to see and signed a certificate
It's also base on the X500 User Schema: rfc2256 of ldap using LDAP attributes as attributes.