field of operations vs theater of operations

field of operations and theater of operations both are nouns.

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

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

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

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

field 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