take on vs undertake

take on and undertake both are verbs.

Word	Noun	Adjective	Verb	Adverb
take on	No	No	Yes	No
undertake	No	No	Yes	No

As verbs, take on and undertake are synonyms defined as:

Other synonyms of take on include tackle.

take on (verb)	undertake (verb)
take on a certain form, attribute, or aspect	promise to do or accomplish
contend against an opponent in a sport, game, or battle	enter into a contractual arrangement
admit into a group or community	enter upon an activity or enterprise
accept as a challenge	accept as a charge
take on titles, offices, duties, responsibilities	accept as a challenge