felicitate vs wish

felicitate is not a noun while wish is a noun.

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

As verbs, wish is a hypernym of felicitate; that is, wish is a word with a broader meaning than felicitate:

Other hypernyms of felicitate include bid.

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

felicitate (verb)	wish (verb)
express congratulations	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