cry out for vs demand

cry out for is not a noun while demand is a noun.

Word	Noun	Adjective	Verb	Adverb
cry out for	No	No	Yes	No
demand	Yes	No	Yes	No

As verbs, demand is a hypernym of cry out for; that is, demand is a word with a broader meaning than cry out for:

Other hypernyms of cry out for include ask, call for, involve, necessitate, need, postulate, require, take.

cry out for (noun)	demand (noun)
	the act of demanding
	required activity
	an urgent or peremptory request
	the ability and desire to purchase goods and services
	a condition requiring relief

cry out for (verb)	demand (verb)
need badly or desperately	request urgently and forcefully
	claim as due or just
	summon to court
	ask to be informed of
	lay legal claim to
	require as useful, just, or proper