enmity vs state of war

enmity and state of war both are nouns.

Word	Noun	Adjective	Verb	Adverb
enmity	Yes	No	No	No
state of war	Yes	No	No	No

As nouns, state of war is a hyponym of enmity; that is, state of war is a word with a more specific, narrower meaning than enmity:

enmity: a state of deep-seated ill-will
state of war: a legal state created by a declaration of war and ended by official declaration during which the international rules of war apply

Other hyponyms of enmity include latent hostility, tension, war, cold war, suspicion.

enmity (noun)	state of war (noun)
the feeling of a hostile person	a legal state created by a declaration of war and ended by official declaration during which the international rules of war apply
a state of deep-seated ill-will