playing area vs playing field

playing area and playing field both are nouns.

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

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

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

Other synonyms of playing area include athletic field, field.

playing area (noun)	playing field (noun)
a piece of land prepared for playing a game	a piece of land prepared for playing a game
	the circumstances under which competition occurs