When running as a daemon and listening for incoming connections, sendmail attempts to look up the true identity of connecting users and hosts. When it can find that information, it saves it in the $_ sendmail macro ($_).

When transporting mail to other hosts, sendmail looks up the MX records for those hosts and connects to the MX records when they are available. If MX records are not available, sendmail connects to A or AAAA addresses.

For recipient and sender syslog lines, the relay= syslog equate shows the name of the corresponding receiving or sending host, followed by the A address, or AAAA address, of that host (if there was one) in square braces:

relay=root@other.site.edu [123.45.67.89]

If the sender is a local user, the login name and localhost will appear in the relay= syslog equate:

relay=bob@localhost

In summary, the relay= syslog equate shows who really accepted or sent the message.