cut back vs shorten

cut back and shorten both are verbs.

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

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

cut back: cut down on; make a reduction in
shorten: make shorter than originally intended; reduce or retrench in length or duration

cut back (verb)	shorten (verb)
place restrictions on	become short or shorter
cut down on; make a reduction in	make shorter than originally intended; reduce or retrench in length or duration
cultivate, tend, and cut back the growth of	reduce in scope while retaining essential elements
return in time	edit by omitting or modifying parts considered indelicate
	make short or shorter