By definition, a
firewall is a system that protects the resources in a private network, while a
router is a device that moves (or routes) data packets among networks.
NAT in routers is simply a byproduct security feature.
With that out of the way, the main differences between a
router and a hardware
firewall is in number of featires and price.
Most low-cost Home/SOHO routers have a built-in
DHCP server and
NAT/PAT, which assigns private, non-routable IP addresses to
LAN clients, and as a byproduct provides simple and effective security features.
Higher priced firewalls/routers provide additional security features, such as Stateful
Packet Inspection,
VPN support, content filters, intrusion attempt logs, etc.
