hostility vs cold war

hostility and cold war both are nouns.

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

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

hostility: 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 hostility include latent hostility, tension, state of war, war, suspicion.

hostility (noun)	cold war (noun)
violent action that is hostile and usually unprovoked	a state of political hostility between countries using means short of armed warfare
a hostile (very unfriendly) disposition
the feeling of a hostile person
a state of deep-seated ill-will