satyr play vs dramatic play

satyr play and dramatic play both are nouns.

Word	Noun	Adjective	Verb	Adverb
satyr play	Yes	No	No	No
dramatic play	Yes	No	No	No

As nouns, dramatic play is a hypernym of satyr play; that is, dramatic play is a word with a broader meaning than satyr play:

satyr play: an ancient Greek burlesque with a chorus of satyrs
dramatic play: a dramatic work intended for performance by actors on a stage

Other hypernyms of satyr play include drama, play.

satyr play (noun)	dramatic play (noun)
an ancient Greek burlesque with a chorus of satyrs	a dramatic work intended for performance by actors on a stage