demand vs cry out for

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

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

As verbs, cry out for is a hyponym of demand; that is, cry out for is a word with a more specific, narrower meaning than demand:

Other hyponyms of demand include claim, exact, take, govern, draw, cost, cry for, compel.

demand (noun)	cry out for (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

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