urge vs desire

urge and desire both are nouns.

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

As nouns, desire is a hypernym of urge; that is, desire is a word with a broader meaning than urge:

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

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