prefer vs promote

prefer and promote both are verbs.

Word	Noun	Adjective	Verb	Adverb
prefer	No	No	Yes	No
promote	No	No	Yes	No

As verbs, promote is a hypernym of prefer; that is, promote is a word with a broader meaning than prefer:

Other hypernyms of prefer include advance, elevate, kick upstairs, raise, upgrade.

prefer (verb)	promote (verb)
select as an alternative over another	make publicity for; try to sell (a product)
like better; value more highly	change a pawn for a better piece by advancing it to the eighth row, or change a checker piece for a more valuable piece by moving it to the row closest to your opponent
promote over another	be changed for a superior chess or checker piece
give preference to one creditor over another	give a promotion to or assign to a higher position
	contribute to the progress or growth of