Note that most current Linux distributions use journald, rather than syslog. Journald has plugins for the syslog wire protocol though. Personally I prefer app names vs LOCAL4 or the other syslog facilities (UUCP is still in there) but YMMV.
If configured to forward messages to syslog, I think systemd does so via the /run/systemd/journal/syslog socket, which is part of syslog.socket. But I believe rsyslog will these days read messages directly out of the journal rather than relying on journald to forward them.
Note that journald internally uses the this socket both for receiving syslog messages, and for forwarding them to any other syslog
edit: formatting