hangnail vs cutis

hangnail and cutis both are nouns.

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

As nouns, cutis is a hypernym of hangnail; that is, cutis is a word with a broader meaning than hangnail:

hangnail: a loose narrow strip of skin near the base of a fingernail; tearing it produces a painful sore that is easily infected
cutis: a natural protective body covering and site of the sense of touch

Other hypernyms of hangnail include skin, tegument.

hangnail (noun)	cutis (noun)
a loose narrow strip of skin near the base of a fingernail; tearing it produces a painful sore that is easily infected	a natural protective body covering and site of the sense of touch