abridge vs cut back

abridge and cut back both are verbs.

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

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

Other hypernyms of abridge include curb, curtail, restrict.

abridge (verb)	cut back (verb)
reduce in scope while retaining essential elements	place restrictions on
lessen, diminish, or curtail	cut down on; make a reduction in
	cultivate, tend, and cut back the growth of
	return in time