languish vs ache

languish is not a noun while ache is a noun.

Word	Noun	Adjective	Verb	Adverb
languish	No	No	Yes	No
ache	Yes	No	Yes	No

As verbs, languish and ache are synonyms defined as:

languish and ache: have a desire for something or someone who is not present

Other synonyms of languish include pine, yearn, yen.

languish (noun)	ache (noun)
	a dull persistent (usually moderately intense) pain

languish (verb)	ache (verb)
become feeble	have a desire for something or someone who is not present
lose vigor, health, or flesh, as through grief	be the source of pain
have a desire for something or someone who is not present	feel physical pain