theatre of operations vs field of operations

theatre of operations and field of operations both are nouns.

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

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

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

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

theatre 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