The difference between a router and a Pix firewall as far as 'firewall services' concern is pretty much the difference between a hardware router and a server that can perform routing between networks.
Routers are dedicated machines which route data between networks while providing some additional services such as firewalling.
Pix Firewalls are dedicated machines for firewalling services in order to protect your network.
Your note is quite a good one and a lot of people do not seem to understand that routers can perform quite a few functions of dedicated firewall devices such as the PIX. Even VPN termination is possible with a router, where its considered a 'standard' feature with PIX machines.
PIX firewalls will allow you to create complex network security layers such as DMZ zones while this is not possible with simple routers. If you take a quick look at the PIX firewall family and their range of supported services, you'll quickly understand why they exist as separate products and not fully built into every router Cisco offers.