dramatic art vs theater

dramatic art and theater both are nouns.

Word	Noun	Adjective	Verb	Adverb
dramatic art	Yes	No	No	No
theater	Yes	No	No	No

As nouns, dramatic art and theater are synonyms defined as:

Other synonyms of dramatic art include dramatics, dramaturgy, theatre.

dramatic art (noun)	theater (noun)
the art of writing and producing plays	a building where theatrical performances or motion-picture shows can be presented
	the art of writing and producing plays
	a region in which active military operations are in progress