hold down vs hold back

hold down and hold back both are verbs.

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

As verbs, hold back is a hypernym of hold down; that is, hold back is a word with a broader meaning than hold down:

Other hypernyms of hold down include hold, keep back, retain.

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