Router and modem?

Question

what is the difference between a router and a modem?

Answer 1

A modulator/demodulator (modem) takes the signal coming in from the broadband provider, and converts it to a useable format such as ethernet or USB. These are called cable modems or dsl modems.  There are also phone modems which do the same thing only for dial-up connections.  

A router distributes this useable signal to more than one computer or device, and may be used to set up more advanced networking such as file sharing, firewalling, etc.

Answer 2

A modem is the link between a computer and a distant computer ie the one at your ISP's site.

A router is a component of a computer network. For example, several computers could be connected to a router via ethernet to make a home/small office network.

Connect the router to the modem and the network now has internet access, for example.

At home I have a laptop and a PS3 that connect to my router wirelessly, my main pc is plugged into the router via ethernet cable. The router is connected to a modem which connects to my isp.  Some devices combine  the router and the modem into one.