cut back vs downsize

cut back and downsize both are verbs.

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

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

cut back (verb)	downsize (verb)
place restrictions on	(of a company) reduce in size or number of employees
cut down on; make a reduction in	design or manufacture in a smaller size
cultivate, tend, and cut back the growth of	dismiss from work
return in time