eat away vs damage

eat away is not a noun while damage is a noun.

Word	Noun	Adjective	Verb	Adverb
eat away	No	No	Yes	No
damage	Yes	No	Yes	No

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

eat away (noun)	damage (noun)
	the act of damaging something or someone
	any harm or injury resulting from a violation of a legal right
	the occurrence of a change for the worse
	loss of military equipment
	the amount of money needed to purchase something

eat away (verb)	damage (verb)
remove soil or rock	inflict damage upon
wear away or erode	suffer or be susceptible to damage