baseball field vs playing field

baseball field and playing field both are nouns.

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

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

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

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