refrain vs hold back

refrain is a noun but hold back is not a noun.

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

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

refrain (noun)	hold back (noun)
the part of a song where a soloist is joined by a group of singers

refrain (verb)	hold back (verb)
choose not to consume	prevent the action or expression of
resist doing something	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