rein vs keep back

rein is a noun but keep back is not a noun.

Word	Noun	Adjective	Verb	Adverb
rein	Yes	No	Yes	No
keep back	No	No	Yes	No

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

Other hypernyms of rein include hold back, keep, restrain.

rein (noun)	keep back (noun)
one of a pair of long straps (usually connected to the bit or the headpiece) used to control a horse
any means of control

rein (verb)	keep back (verb)
keep in check	prevent the action or expression of
stop or slow up one's horse or oneself by or as if by pulling the reins	hold back; refuse to hand over or share
stop or check by or as if by a pull at the reins	secure and keep for possible future use or application
control and direct with or as if by reins