The difference between a router and a modem lies in their distinct functions within a network. A modem (modulator-demodulator) connects to the internet service provider and converts signals for internet access. In contrast, a router connects multiple devices within a network and directs data traffic between those devices and the modem. While the modem establishes the initial internet connection, the router ensures that data is routed efficiently to various devices, enabling seamless communication within the local network and access to the internet.