war god vs immortal

war god and immortal both are nouns.

Word	Noun	Adjective	Verb	Adverb
war god	Yes	No	No	No
immortal	Yes	Yes	No	No

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

war god: a god worshipped as giving victory in war
immortal: any supernatural being worshipped as controlling some part of the world or some aspect of life or who is the personification of a force

Other hypernyms of war god include deity, divinity, god.

war god (noun)	immortal (noun)
a god worshipped as giving victory in war	any supernatural being worshipped as controlling some part of the world or some aspect of life or who is the personification of a force
	a person (such as an author) of enduring fame

war god (adjective)	immortal (adjective)
	not subject to death