let go vs let out

let go and let out both are verbs.

Word	Noun	Adjective	Verb	Adverb
let go	No	No	Yes	No
let out	No	No	Yes	No

As verbs, let out is a hyponym of let go; that is, let out is a word with a more specific, narrower meaning than let go:

let go (verb)	let out (verb)
release, as from one's grip	make (clothes) larger
be relaxed	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