demand vs cry for

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

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

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

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

demand (noun)	cry 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 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