crying vs wailing

crying and wailing both are nouns.

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

As nouns, wailing is a hyponym of crying; that is, wailing is a word with a more specific, narrower meaning than crying:

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

Other hyponyms of crying include snivel, sniveling, sob, sobbing, bawling.

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

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