hatchet vs ax

hatchet and ax both are nouns.

Word	Noun	Adjective	Verb	Adverb
hatchet	Yes	No	No	No
ax	Yes	No	Yes	No

As nouns, ax is a hypernym of hatchet; that is, ax is a word with a broader meaning than hatchet:

hatchet: a small ax with a short handle used with one hand (usually to chop wood)
ax: an edge tool with a heavy bladed head mounted across a handle

Other hypernyms of hatchet include axe.

hatchet (noun)	ax (noun)
a small ax with a short handle used with one hand (usually to chop wood)	an edge tool with a heavy bladed head mounted across a handle
weapon consisting of a fighting ax; used by North American Indians

hatchet (verb)	ax (verb)
	terminate
	chop or split with an ax