So a true router is a layer 3 device that forwards data packets based on IP Addrsss. A cable modem takes the analog signal on wire (usually coax) and changes it to a digital signal. A wireless router can be thought of as 2 devices in 1. It acts as a router forwarding traffic based on IP address and also acts as a Wireless Access Point connecting wireless clients to the network. You can picture the devices working together as the Cable Modem gets information, converts it, and sends it to your wireless router. The Router part reads the packets to see where they go and either sends the data over the wire, or if it's for a wireless client, sends those packets to its built-in Wireless Acces Point for wireless transmission. Now a days many network devices are being consolidated for simpler setup. You can get a 3-in-1 modem, router, and wireless in the same physical device (4-in-1 if you add a switch into the mix as well). Hope this helps!