hand axe vs hand ax

hand axe and hand ax both are nouns.

Word	Noun	Adjective	Verb	Adverb
hand axe	Yes	No	No	No
hand ax	Yes	No	No	No

As nouns, hand axe and hand ax are synonyms defined as:

hand axe and hand ax: a stone tool with a cutting edge; the stone is held in the hand and used for chopping

hand axe (noun)	hand ax (noun)
a stone tool with a cutting edge; the stone is held in the hand and used for chopping	a stone tool with a cutting edge; the stone is held in the hand and used for chopping