The destination syslog server probably just uses "syslog.log" as the default filename for the syslog stream, so yes, it is different.
If you want to split the resulting logfile then you could filter by keywords on the destination syslog server, similar to how it's done here:
http://alpacapowered.wordpress.com/2012/10/08/vma-as-syslog-server/
I'm not sure about 4.1 but I think it should work the same way.