bell push vs push button

bell push and push button both are nouns.

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

As nouns, push button is a hypernym of bell push; that is, push button is a word with a broader meaning than bell push:

Other hypernyms of bell push include button, push.

bell push (noun)	push button (noun)
a button that is pushed to ring a bell	an electrical switch operated by pressing