Have I worked it out
A simple answer to your question is tuned circuits. Both the transmitter and the the receiver require a tuned circuit of some form. An inductor and a capacitor.
When you are changing stations on a broadcast receiver you are adjusting the frequency of one or more tuned or resonate circuits. For exact and stable frequencies whether it be for receive or transmit there is bound to be a quartz crystal somewhere in the frequency determining circuitry of either unit. The quartz crystal is a form of a resonate circuit, only it is highly accurate and very stable, where as regular tuned or resonate circuits are not as accurate or stable.