The main difference between the two firewalls is that stateful inspection systems maintain a state table, allowing them to keep track of all open connections through a firewall, while packet-filtering firewalls do not. When traffic arrives, the system compares the traffic to the state table, determining whether it is part of an established connection.
The only place you'll likely see packet filtering in today's environment is at an Internet-facing router. These devices often implement a basic packet-filtering rule set to weed out obviously unwanted traffic and reduce the load on a stateful inspection firewall immediately behind the router.
This was first published in October 2006