let down vs come short

let down and come short both are verbs.

Word	Noun	Adjective	Verb	Adverb
let down	No	No	Yes	No
come short	No	No	Yes	No

As verbs, come short is a hyponym of let down; that is, come short is a word with a more specific, narrower meaning than let down:

Other hyponyms of let down include betray, fail, fall short, disenchant, disillusion.

let down (verb)	come short (verb)
fail to meet the hopes or expectations of	fail to meet (expectations or standards)
move something or somebody to a lower position