hee-haw vs utter

hee-haw is a noun but utter is not a noun.

Word	Noun	Adjective	Verb	Adverb
hee-haw	Yes	No	Yes	No
utter	No	Yes	Yes	No

As verbs, utter is a hypernym of hee-haw; that is, utter is a word with a broader meaning than hee-haw:

Other hypernyms of hee-haw include emit, let loose, let out.

hee-haw (noun)	utter (noun)
a loud laugh that sounds like a horse neighing

hee-haw (adjective)	utter (adjective)
	complete and absolute
	without qualification; used informally as (often pejorative) intensifiers

hee-haw (verb)	utter (verb)
braying characteristic of donkeys	express in speech
	articulate; either verbally or with a cry, shout, or noise
	express audibly; utter sounds (not necessarily words)
	put into circulation