handset vs telephone set

handset and telephone set both are nouns.

Word	Noun	Adjective	Verb	Adverb
handset	Yes	No	No	No
telephone set	Yes	No	No	No

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

handset: telephone set with the mouthpiece and earpiece mounted on a single handle
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 handset include phone, telephone.

handset (noun)	telephone set (noun)
telephone set with the mouthpiece and earpiece mounted on a single handle	electronic equipment that converts sound into electrical signals that can be transmitted over distances and then converts received signals back into sounds