palaestra vs playing field

palaestra and playing field both are nouns.

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

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

palaestra: a public place in ancient Greece or Rome devoted to the training of wrestlers and other athletes
playing field: a piece of land prepared for playing a game

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

palaestra (noun)	playing field (noun)
a public place in ancient Greece or Rome devoted to the training of wrestlers and other athletes	a piece of land prepared for playing a game
	the circumstances under which competition occurs