take up arms vs war

take up arms is not a noun while war is a noun.

Word	Noun	Adjective	Verb	Adverb
take up arms	No	No	Yes	No
war	Yes	No	Yes	No

As verbs, war is a hypernym of take up arms; that is, war is a word with a broader meaning than take up arms:

take up arms (noun)	war (noun)
	the waging of armed conflict against an enemy
	a concerted campaign to end something that is injurious
	an active struggle between competing entities
	a legal state created by a declaration of war and ended by official declaration during which the international rules of war apply

take up arms (verb)	war (verb)
commence hostilities	make or wage war