wailing vs crying

wailing and crying both are nouns.

Word	Noun	Adjective	Verb	Adverb
wailing	Yes	Yes	No	No
crying	Yes	Yes	No	No

As nouns, crying is a hypernym of wailing; that is, crying is a word with a broader meaning than wailing:

wailing: loud cries made while weeping
crying: the process of shedding tears (usually accompanied by sobs or other inarticulate sounds)

Other hypernyms of wailing include tears, weeping.

wailing (noun)	crying (noun)
loud cries made while weeping	the process of shedding tears (usually accompanied by sobs or other inarticulate sounds)

wailing (adjective)	crying (adjective)
vocally expressing grief or sorrow or resembling such expression	conspicuously and outrageously bad or reprehensible
	demanding attention