X.509 – How Is Certificate Chain of Trust “Subject Name”-“Issuer Name” Match Comparison Made?

I keep reading that in an X.509 certificate chain of trust that the "Issuer Name" in a certificate that has been signed by the Issuer must "match" the "Subject Name" of the Issuer’s certificate. Exactly how is this match determined? Do all of the RDNs (Relative Distinguished Names) have to match between both the Subject Name and Issuer Name or is the match determined solely by the RDNs that are present in the Issuer certificate’s Subject Name, or is some other match algorithm at work?