wish vs wishing

wish and wishing both are nouns.

Word	Noun	Adjective	Verb	Adverb
wish	Yes	No	Yes	No
wishing	Yes	No	No	No

As nouns, wish and wishing are synonyms defined as:

Other synonyms of wish include want.

wish (noun)	wishing (noun)
the particular preference that you have	a specific feeling of desire
an expression of some desire or inclination
(usually plural) a polite expression of desire for someone's welfare
a specific feeling of desire

wish (verb)	wishing (verb)
invoke upon
order politely; express a wish for
make or express a wish
feel or express a desire or hope concerning the future or fortune of
to hope, to desire or to prefer to have something, or to do something