weeping vs wailing

weeping and wailing both are nouns.

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

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

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

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

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

weeping (adjective)	wailing (adjective)
showing sorrow	vocally expressing grief or sorrow or resembling such expression
having branches or flower heads that bend downward