war vs take up arms

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

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

As verbs, take up arms is a hyponym of war; that is, take up arms is a word with a more specific, narrower meaning than war:

Other hyponyms of war include blitzkrieg, go to war, take arms.

war (noun)	take up arms (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

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