desire vs urge

desire and urge both are nouns.

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

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

desire (noun)	urge (noun)
an inclination to want things	a strong restless desire
the feeling that accompanies an unsatisfied state	an instinctive motive
something that is desired

desire (verb)	urge (verb)
feel or have a desire for; want strongly	force or impel in an indicated direction
express a desire for	spur on or encourage especially by cheers and shouts
expect and wish	push for something