battlefield vs field of battle

battlefield and field of battle both are nouns.

Word	Noun	Adjective	Verb	Adverb
battlefield	Yes	No	No	No
field of battle	Yes	No	No	No

As nouns, battlefield and field of battle are synonyms defined as:

battlefield and field of battle: a region where a battle is being (or has been) fought

Other synonyms of battlefield include battleground, field, field of honor.

battlefield (noun)	field of battle (noun)
a region where a battle is being (or has been) fought	a region where a battle is being (or has been) fought