theatre of operations vs theater of operations

theatre of operations and theater of operations both are nouns.

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

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

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

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

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