shave vs cut back

shave is a noun but cut back is not a noun.

Word	Noun	Adjective	Verb	Adverb
shave	Yes	No	Yes	No
cut back	No	No	Yes	No

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

Other hypernyms of shave include bring down, cut, cut down, reduce, trim, trim back, trim down.

shave (noun)	cut back (noun)
the act of removing hair with a razor

shave (verb)	cut back (verb)
remove body hair with a razor	place restrictions on
touch the surface of lightly	cut down on; make a reduction in
cut closely	cultivate, tend, and cut back the growth of
cut or remove with or as if with a plane	return in time
make shavings of or reduce to shavings
cut the price of