barber's itch vs tinea

barber's itch and tinea both are nouns.

Word	Noun	Adjective	Verb	Adverb
barber's itch	Yes	No	No	No
tinea	Yes	No	No	No

As nouns, tinea is a hypernym of barber's itch; that is, tinea is a word with a broader meaning than barber's itch:

barber's itch: fungal infection of the face and neck
tinea: infections of the skin or nails caused by fungi and appearing as itching circular patches

Other hypernyms of barber's itch include ringworm, roundworm.

barber's itch (noun)	tinea (noun)
fungal infection of the face and neck	infections of the skin or nails caused by fungi and appearing as itching circular patches