theater in the round vs arena theater

theater in the round and arena theater both are nouns.

Word	Noun	Adjective	Verb	Adverb
theater in the round	Yes	No	No	No
arena theater	Yes	No	No	No

As nouns, theater in the round and arena theater are synonyms defined as:

theater in the round and arena theater: a theater arranged with seats around at least three sides of the stage

theater in the round (noun)	arena theater (noun)
a theater arranged with seats around at least three sides of the stage	a theater arranged with seats around at least three sides of the stage