A mechanical buzzer works by powering an electromagnet which moves some contact arm to disconnect power from the electromagnet and thus the contact arm moves back to connect power to the electromagnet. The arm movement may also vibrate a membrane of some sorts to better couple the arm movement to sound waves in air.
As the electromagnet is a coil and coils have inductance, and disconnecting inductive load makes the magnetic field to collapse rapidly and it creates back-EMF or inductive kick which basically tries to keep the current flowing, it will raise the voltage over the contacts and it may spark and sparks emit electromagnetic radiation. Even if it does not spark, it will consume current while the magnet operates and does not consume current when the magnet does not operate so the buzzer supply wires are like a small current loop antenna that transmits magnetic pulses at the buzzing frequency.
Basically, mechanical buzzers are just small devices that radiate bursts of broadband electromagnetic interference, and the radio will also receive the electromagnetic interference pulses as it would receive any other radio signal so you can hear it on the radio speakers.
A piezo buzzer just has an electronic oscillator which drives voltage to a piezoelectric disc which will deform under voltage to transmit acoustic energy so there is no mechanism which would transmit electromagnetic interference out.