push-button radio vs radio set

push-button radio and radio set both are nouns.

Word	Noun	Adjective	Verb	Adverb
push-button radio	Yes	No	No	No
radio set	Yes	No	No	No

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

push-button radio: a radio receiver that can be tuned by pressing buttons
radio set: an electronic receiver that detects and demodulates and amplifies transmitted signals

Other hypernyms of push-button radio include radio, radio receiver, receiving set, tuner, wireless.

push-button radio (noun)	radio set (noun)
a radio receiver that can be tuned by pressing buttons	an electronic receiver that detects and demodulates and amplifies transmitted signals