theater of operations vs field of operations

theater of operations and field of operations both are nouns.

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

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

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

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

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