playing field vs playing area

playing field and playing area both are nouns.

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

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

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

Other synonyms of playing field include athletic field, field.

playing field (noun)	playing area (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