lament vs wail

lament and wail both are nouns.

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

As nouns, lament and wail are synonyms defined as:

Other synonyms of lament include lamentation, plaint.

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

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