pay-phone vs telephone set

pay-phone and telephone set both are nouns.

Word	Noun	Adjective	Verb	Adverb
pay-phone	Yes	No	No	No
telephone set	Yes	No	No	No

As nouns, telephone set is a hypernym of pay-phone; that is, telephone set is a word with a broader meaning than pay-phone:

pay-phone: a coin-operated telephone
telephone set: electronic equipment that converts sound into electrical signals that can be transmitted over distances and then converts received signals back into sounds

Other hypernyms of pay-phone include phone, telephone.

pay-phone (noun)	telephone set (noun)
a coin-operated telephone	electronic equipment that converts sound into electrical signals that can be transmitted over distances and then converts received signals back into sounds