hee-haw vs let out

hee-haw is a noun but let out is not a noun.

Word	Noun	Adjective	Verb	Adverb
hee-haw	Yes	No	Yes	No
let out	No	No	Yes	No

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

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

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

hee-haw (verb)	let out (verb)
braying characteristic of donkeys	make (clothes) larger
	make known to the public information that was previously known only to a few people or that was meant to be kept a secret
	express audibly; utter sounds (not necessarily words)
	bring out of a specific state