Statefull vs Stateless Packet Filtering

The biggest difference between simple IP filtering and stateful IP filtering is that simple IP filters have no recollection of packets that have already passed through the filter. Every packet is handled on an individual basis. Previously forwarded packets belonging to a connection have no bearing on the filter's decision to forward or drop the packet.

Stateful firewall (any firewall that performs stateful packet inspection or stateful inspection) is a firewall that keeps track of the state of network connections (such as TCP streams) travelling across it. The firewall is programmed to distinguish legitimate packets for different types of connections. Only packets matching a known connection state will be allowed by the firewall; others will be rejected.

stateless firewall is a firewall that treats each network frame (or packet) in isolation. Such a firewall has no way of knowing if any given packet is part of an existing connection, is trying to establish a new connection, or is just a rogue packet.