My understanding (based on scanning the forums and not on extensive personal testing) is that 'private server' mode leaves more ports open than server-gateway mode, under the assumption that the server is 'private' and therefore less exposed...
It isn't 'serving' to the internet, but is still assumed to be 'serving' to the local network.
I would definitely expect a sme server in 'private server' mode to respond on ports 80, 21, 53, 139, 389, 443, 980.
25, 22, 110, 143, 465, 995, 993 can be disabled in server-manager (smtp, ssh, pop3, imap, smtps, pop3s, imaps)
Mine looks like it's also listening on 515, 548, 783, 26 and 4700...