theater vs dramatic art

theater and dramatic art both are nouns.

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

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

Other synonyms of theater include dramatics, dramaturgy, theatre.

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