field of operations vs theatre of operations

field of operations and theatre of operations both are nouns.

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

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

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

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

field 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