promise vs undertake

promise is a noun but undertake is not a noun.

Word	Noun	Adjective	Verb	Adverb
promise	Yes	No	Yes	No
undertake	No	No	Yes	No

As verbs, undertake is a hyponym of promise; that is, undertake is a word with a more specific, narrower meaning than promise:

Other hyponyms of promise include pledge, plight, swear off, contract, guarantee.

promise (noun)	undertake (noun)
grounds for feeling hopeful about the future
a verbal commitment by one person to another agreeing to do (or not to do) something in the future

promise (verb)	undertake (verb)
make a promise or commitment	promise to do or accomplish
promise to undertake or give	enter into a contractual arrangement
make a prediction about; tell in advance	enter upon an activity or enterprise
give grounds for expectations	accept as a charge
	accept as a challenge