playing vs performing arts

playing and performing arts both are nouns.

Word	Noun	Adjective	Verb	Adverb
playing	Yes	No	No	No
performing arts	Yes	No	No	No

As nouns, performing arts is a hypernym of playing; that is, performing arts is a word with a broader meaning than playing:

Other hypernyms of playing include activity.

playing (noun)	performing arts (noun)
the action of taking part in a game or sport or other recreation	arts or skills that require public performance
the act of playing a musical instrument
the performance of a part or role in a drama