desire vs yearn

desire is a noun but yearn is not a noun.

Word	Noun	Adjective	Verb	Adverb
desire	Yes	No	Yes	No
yearn	No	No	Yes	No

As verbs, yearn is a hyponym of desire; that is, yearn is a word with a more specific, narrower meaning than desire:

desire (noun)	yearn (noun)
an inclination to want things
the feeling that accompanies an unsatisfied state
something that is desired

desire (verb)	yearn (verb)
feel or have a desire for; want strongly	desire strongly or persistently
express a desire for	have a desire for something or someone who is not present
expect and wish	have affection for; feel tenderness for