enmity vs cold war

enmity and cold war both are nouns.

Word	Noun	Adjective	Verb	Adverb
enmity	Yes	No	No	No
cold war	Yes	No	No	No

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

enmity: a state of deep-seated ill-will
cold war: a state of political hostility between countries using means short of armed warfare

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

enmity (noun)	cold war (noun)
the feeling of a hostile person	a state of political hostility between countries using means short of armed warfare
a state of deep-seated ill-will