burn off vs eat up

burn off and eat up both are verbs.

Word	Noun	Adjective	Verb	Adverb
burn off	No	No	Yes	No
eat up	No	No	Yes	No

As verbs, eat up is a hypernym of burn off; that is, eat up is a word with a broader meaning than burn off:

Other hypernyms of burn off include consume, deplete, eat, exhaust, expend, run through, use, use up, wipe out.

burn off (verb)	eat up (verb)
clear land of its vegetation by burning it off	finish eating all the food on one's plate or on the table
use up (energy)	use up (resources or materials)
	enclose or envelop completely, as if by swallowing