theater of operations vs theatre of operations

theater of operations and theatre of operations both are nouns.

Word	Noun	Adjective	Verb	Adverb
theater of operations	Yes	No	No	No
theatre of operations	Yes	No	No	No

As nouns, theater of operations and theatre of operations are synonyms defined as:

theater of operations and theatre of operations: a region in which active military operations are in progress

Other synonyms of theater of operations include field, field of operations, theater, theatre.

theater of operations (noun)	theatre of operations (noun)
a region in which active military operations are in progress	a region in which active military operations are in progress