playing area vs athletic field

playing area and athletic field both are nouns.

Word	Noun	Adjective	Verb	Adverb
playing area	Yes	No	No	No
athletic field	Yes	No	No	No

As nouns, playing area and athletic field are synonyms defined as:

playing area and athletic field: a piece of land prepared for playing a game

Other synonyms of playing area include field, playing field.

playing area (noun)	athletic field (noun)
a piece of land prepared for playing a game	a piece of land prepared for playing a game