hangnail vs agnail

hangnail and agnail both are nouns.

Word	Noun	Adjective	Verb	Adverb
hangnail	Yes	No	No	No
agnail	Yes	No	No	No

As nouns, hangnail and agnail are synonyms defined as:

hangnail and agnail: a loose narrow strip of skin near the base of a fingernail; tearing it produces a painful sore that is easily infected

hangnail (noun)	agnail (noun)
a loose narrow strip of skin near the base of a fingernail; tearing it produces a painful sore that is easily infected	a loose narrow strip of skin near the base of a fingernail; tearing it produces a painful sore that is easily infected