hold back vs hold down

hold back and hold down both are verbs.

Word	Noun	Adjective	Verb	Adverb
hold back	No	No	Yes	No
hold down	No	No	Yes	No

As verbs, hold down is a hyponym of hold back; that is, hold down is a word with a more specific, narrower meaning than hold back:

hold back (verb)	hold down (verb)
prevent the action or expression of	restrain
hold back, as of a danger or an enemy; check the expansion or influence of	keep
hold back; keep from being perceived by others
secure and keep for possible future use or application
wait before acting
refrain from doing