Router

A Device which acts as an interface betweeen two networks.
It forwards packets based on IP addresses between your ISP's router and either your LAN or your single PC.
A router learns more about the networks to which it is connected and can be more selective about the packets it passes on.
A router can also select the best route for packets to take in large interconnected networks.

Modem

Modem is a device that transmits and receives data over the plain old telephone system's (POTS) analogue lines.
It allows your PC to connect to your ISP using the Internet Protocol.
The modem acts as a "bridge" between your PC and your ISP.
The dynamic or static public IP address which your modem obtains from your ISP is passed on to your PC.
Modem forwards packets based on hardware level MAC addresses between your ISP's router (and the Internet) and your PC.

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