play around vs busy

play around is not an adjective while busy is an adjective.

Word	Noun	Adjective	Verb	Adverb
play around	No	No	Yes	No
busy	No	Yes	Yes	No

As verbs, busy is a hypernym of play around; that is, busy is a word with a broader meaning than play around:

Other hypernyms of play around include occupy.

play around (adjective)	busy (adjective)
	actively or fully engaged or occupied
	overcrowded or cluttered with detail
	intrusive in a meddling or offensive manner
	(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)
	crowded with or characterized by much activity

play around (verb)	busy (verb)
commit adultery	keep busy with
work with in an amateurish manner