hue and cry vs shout

hue and cry and shout both are nouns.

Word	Noun	Adjective	Verb	Adverb
hue and cry	Yes	No	No	No
shout	Yes	No	Yes	No

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

Other hypernyms of hue and cry include call, cry, outcry, vociferation, yell.

hue and cry (noun)	shout (noun)
loud and persistent outcry from many people	a loud utterance; often in protest or opposition

hue and 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