When in doubt, check the manufacturer's datasheet. (Reliable suppliers will give you a manufacturer's part number or a link to the datasheet.)
A (active) buzzer will have a DC voltage rating and fixed-frequency.
A transducer will have a frequency range and an AC voltage rating (or AC voltage sensitivity such as 90dB @ 1V RMS @ 2kHz.) Most transducers are used as speakers but there are acoustic-guitar microphones and drum "triggers" made from piezo elements. Some cheap "ceramic" phono pickups are piezo's.
An "element" wouldn't have any electronics and probably no case/housing.