burn up vs eat up

burn up and eat up both are verbs.

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

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

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

burn up (verb)	eat up (verb)
burn completely; be consumed or destroyed by fire	finish eating all the food on one's plate or on the table
use up (energy)	use up (resources or materials)
burn brightly	enclose or envelop completely, as if by swallowing