Routers ROUTE. Use one when you want to route something. It lets traffic in.
A firewall blocks traffic. Use one when you want to stop traffic.
The two should not be used interchangeably. Cheap routers give you very little protection from the bad guys in the Internet, and should not be shoehorned into that kind of service. Most inexpensive routers do NOT usually have a firewall built in.
A firewall is a separate bit of software or hardware.
There are a lot of RBS Providers out there having unprotected TCP/IP who could catch something just any time now.
Remember - Routers Route. Firewalls Protect. You need both. Oh, and you also need virus protection.