football field vs playing field

football field and playing field both are nouns.

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

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

Other hypernyms of football field include athletic field, field, playing area.

football field (noun)	playing field (noun)
the playing field on which football is played	a piece of land prepared for playing a game
	the circumstances under which competition occurs