is a modem and router the same thing?

A modem is used to connect you to the internet, a router splits an internet connection between multiple computers... basically
 
Not exactly....the cable comes into the house, and connects to the modem. The modem in turn can connect to just one computer using a cord (cat5). A router can that that cord (cat5) from the modem, and make it so that multiple computers can use the connection. So a modem takes in the connection, and the router splits it up for multiple computers. Two different pcs. of hardware.
 
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