four-act play vs dramatic play

four-act play and dramatic play both are nouns.

Word	Noun	Adjective	Verb	Adverb
four-act play	Yes	No	No	No
dramatic play	Yes	No	No	No

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

four-act play: An act structure found in early twentieth century stage dramas, such as those of Anton Chekhov and Henrik Ibsen.
dramatic play: a dramatic work intended for performance by actors on a stage

Other hypernyms of four-act play include drama, play.

four-act play (noun)	dramatic play (noun)
An act structure found in early twentieth century stage dramas, such as those of Anton Chekhov and Henrik Ibsen.	a dramatic work intended for performance by actors on a stage