In firewall terms, "a session is a session."
A session comprises a connection between two endpoints. Usually the word "session" refers to TCP since it's a connection-based protocol. However, firewalls also create sessions for UDP and ICMP traffic (and others... just an example) so that they can build a state table and permit bi-directional traffic without having to create explicit bi-directional rules.
When sizing a firewall, look not only at the total sessions, but also the new sessions per second rate (also known as the ramp-up rate). That number will determine how fast the firewall can accept new connections into your network.
The SSG550 is a good machine built on the venerable ScreenOS. It can also be converted to Junos, if you're really adventurous. Personally -- I'd leave it on ScreenOS.
If your webserver shows an average of 13,000 connections at any given time, I might say the 550M could even be overkill, but that's going to depend also on your bandwidth needs.