cold war vs enmity

cold war and enmity both are nouns.

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

As nouns, enmity is a hypernym of cold war; that is, enmity is a word with a broader meaning than cold war:

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

Other hypernyms of cold war include antagonism, hostility.

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