lamenter vs wailer

lamenter and wailer both are nouns.

Word	Noun	Adjective	Verb	Adverb
lamenter	Yes	No	No	No
wailer	Yes	No	No	No

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

lamenter: a person who is feeling grief (as grieving over someone who has died)
wailer: a mourner who utters long loud high-pitched cries

Other hyponyms of lamenter include bearer, pallbearer, weeper.

lamenter (noun)	wailer (noun)
a person who is feeling grief (as grieving over someone who has died)	a mourner who utters long loud high-pitched cries