All traffic that goes through the ASA is inspected using the Adaptive Security Algorithm and is either allowed through or dropped. Although we can use ACLs on a router interface that can check the source IP address, destination IP address, the protocol and source and destination ports; these are not the main functions of the router. The five fields are commonly called the tuple.
The firewall does a far deeper inspection of the packets, as it is a dedicated device to perform the security functions.
Some firewalls monitor the traffic in each direction without maintaining any state of the TCP connections, but monitoring traffic as per the defined security policies. Such firewalls are called stateless firewalls.
The other ...