hatchet vs half hatchet

hatchet and half hatchet both are nouns.

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

As nouns, half hatchet is a hyponym of hatchet; that is, half hatchet is a word with a more specific, narrower meaning than hatchet:

hatchet: a small ax with a short handle used with one hand (usually to chop wood)
half hatchet: a hatchet with a half axe head

Other hyponyms of hatchet include broad hatchet, claw hatchet.

hatchet (noun)	half hatchet (noun)
a small ax with a short handle used with one hand (usually to chop wood)	a hatchet with a half axe head
weapon consisting of a fighting ax; used by North American Indians