hand-down vs hand-me-down

hand-down is not a noun while hand-me-down is a noun.

Word	Noun	Adjective	Verb	Adverb
hand-down	No	Yes	No	No
hand-me-down	Yes	Yes	No	No

As adjectives, hand-down and hand-me-down are synonyms defined as:

hand-down (noun)	hand-me-down (noun)
	outgrown garment passed down from one person to another

hand-down (adjective)	hand-me-down (adjective)
passed on from one person to another	passed on from one person to another