wail vs lament

wail and lament both are nouns.

Word	Noun	Adjective	Verb	Adverb
wail	Yes	No	Yes	No
lament	Yes	No	Yes	No

As nouns, wail and lament are synonyms defined as:

Other synonyms of wail include lamentation, plaint.

wail (noun)	lament (noun)
a cry of sorrow and grief	a mournful poem; a lament for the dead
	a song or hymn of mourning composed or performed as a memorial to a dead person
	a cry of sorrow and grief

wail (verb)	lament (verb)
cry weakly or softly	regret strongly
emit long loud cries	express grief verbally