The Remote Facility names are simply labels. You can create different audit filters and have these sent to a syslog server with different facility names so that you can tell them apart via the syslog server software you are using. They are only labels.
You can send all the audit to a syslog server if you'd like. It may overwhelm your syslog server, though.
SNMP is different from syslog but you mentioned them both in your post.