Would a modem be like a router?

1. They are not the same.

2. A modem is a device used to send information to and receive from another computer or network. Modem stands for MOdulator/DEModulator and is normally used to send over phone lines. There are other applications (like satellite links, etc).

3. A router does just what it says. It routes signals on a network. One in a home application is normally used to share one access point to the internet between multiple computers.

This is a bit of a simple answer but hopefully you get the idea!