thumbhole vs finger hole

thumbhole and finger hole both are nouns.

Word	Noun	Adjective	Verb	Adverb
thumbhole	Yes	No	No	No
finger hole	Yes	No	No	No

As nouns, finger hole is a hypernym of thumbhole; that is, finger hole is a word with a broader meaning than thumbhole:

thumbhole (noun)	finger hole (noun)
a finger hole made to fit the thumb (as in a bowling ball)	a hole for inserting a finger
the hole in a woodwind that is closed and opened with the thumb	one of a series of holes in a woodwind instrument; pitch changes when a finger covers it