A simple way for devices to communicate through wires is to use a fixed voltage for each value. This is easy for devices to understand, but it does not travel well through a very long wire like a phone line or a cable. Modulation is a much more complex way to send the signal, but it can go through long wires very easily.
A modem (short for modulator-demolulator) translates between the modulated signal in the line and the simpler signal used by your computer.
A router communicates only in the simple signal, but it can do so with many different devices. (It routs the data to and from whatever uses it)
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