Authenticator may refer to NIST.SP.800-63B or to the FIDO Authenticator.
To LDAPWiki this is all just very confusing as an Authenticator is nothing different than a claim (i.e. Credential) that is typically tied to a specific Authentication Method during the Credential Enrollment process by the Identity Proofing process.
Typically in Password-based Authentication, there are two Entities:
The Authentication Method determines how Validation of these two claims is performed and this process is AuthenticationIn previous editions of NIST.SP.800-63 versions, this was referred to as a token.