battle cry vs shout

battle cry and shout both are nouns.

Word	Noun	Adjective	Verb	Adverb
battle cry	Yes	No	No	No
shout	Yes	No	Yes	No

As nouns, shout is a hypernym of battle cry; that is, shout is a word with a broader meaning than battle cry:

Other hypernyms of battle cry include call, cry, outcry, vociferation, yell.

battle cry (noun)	shout (noun)
a yell intended to rally a group of soldiers in battle	a loud utterance; often in protest or opposition
a slogan used to rally support for a cause

battle cry (verb)	shout (verb)
	utter in a loud voice; talk in a loud voice (usually denoting characteristic manner of speaking)
	utter a sudden loud cry
	utter aloud; often with surprise, horror, or joy
	use foul or abusive language towards