damage vs eat away

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

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

As verbs, eat away is a hyponym of damage; that is, eat away is a word with a more specific, narrower meaning than damage:

damage (noun)	eat away (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

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