push button vs doorbell

push button and doorbell both are nouns.

Word	Noun	Adjective	Verb	Adverb
push button	Yes	No	No	No
doorbell	Yes	No	No	No

As nouns, doorbell is a hyponym of push button; that is, doorbell is a word with a more specific, narrower meaning than push button:

push button: an electrical switch operated by pressing
doorbell: a push button at an outer door that gives a ringing or buzzing signal when pushed

Other hyponyms of push button include bell push, bell, buzzer, horn button, mouse button, panic button, reset button.

push button (noun)	doorbell (noun)
an electrical switch operated by pressing	a push button at an outer door that gives a ringing or buzzing signal when pushed