war god vs god

war god and god both are nouns.

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

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

war god: a god worshipped as giving victory in war
god: 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, immortal.

war god (noun)	god (noun)
a god worshipped as giving victory in war	a material effigy that is worshipped
	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 man of such superior qualities that he seems like a deity to other people