have a good time vs enjoy

have a good time and enjoy both are verbs.

Word	Noun	Adjective	Verb	Adverb
have a good time	No	No	Yes	No
enjoy	No	No	Yes	No

As verbs, enjoy is a hypernym of have a good time; that is, enjoy is a word with a broader meaning than have a good time:

Other hypernyms of have a good time include delight, revel.

have a good time (verb)	enjoy (verb)
enjoy oneself greatly	take delight in
	have benefit from
	derive or receive pleasure from; get enjoyment from; take pleasure in
	get pleasure from
	have for one's benefit