handgrip vs ax handle

handgrip and ax handle both are nouns.

Word	Noun	Adjective	Verb	Adverb
handgrip	Yes	No	No	No
ax handle	Yes	No	No	No

As nouns, ax handle is a hyponym of handgrip; that is, ax handle is a word with a more specific, narrower meaning than handgrip:

handgrip: the appendage to an object that is designed to be held in order to use or move it
ax handle: the handle of an ax

handgrip (noun)	ax handle (noun)
the appendage to an object that is designed to be held in order to use or move it	the handle of an ax