ache vs languish

ache is a noun but languish is not a noun.

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

As verbs, ache and languish are synonyms defined as:

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

Other synonyms of ache include pine, yearn, yen.

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

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