run around vs frolic

run around is not a noun while frolic is a noun.

Word	Noun	Adjective	Verb	Adverb
run around	No	No	Yes	No
frolic	Yes	No	Yes	No

As verbs, run around and frolic are synonyms defined as:

Other synonyms of run around include cavort, disport, frisk, gambol, lark, lark about, rollick, romp, skylark, sport.

run around (noun)	frolic (noun)
	gay or light-hearted recreational activity for diversion or amusement

run around (verb)	frolic (verb)
play boisterously	play boisterously