desire vs wish well

desire is a noun but wish well is not a noun.

Word	Noun	Adjective	Verb	Adverb
desire	Yes	No	Yes	No
wish well	No	No	Yes	No

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

desire: feel or have a desire for; want strongly
wish well: feel or express a desire or hope concerning the future or fortune of

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

desire (verb)	wish well (verb)
feel or have a desire for; want strongly	feel or express a desire or hope concerning the future or fortune of
express a desire for
expect and wish