widen vs vary

widen and vary both are verbs.

Word	Noun	Adjective	Verb	Adverb
widen	No	No	Yes	No
vary	No	No	Yes	No

As verbs, vary is a hypernym of widen; that is, vary is a word with a broader meaning than widen:

widen: make (clothes) larger
vary: become different in some particular way, without permanently losing one's or its former characteristics or essence

Other hypernyms of widen include alter, change.

widen (verb)	vary (verb)
become broader or wider or more extensive	become different in some particular way, without permanently losing one's or its former characteristics or essence
extend in scope or range or area	make something more diverse and varied
make wider	be at variance with; be out of line with
make (clothes) larger	be subject to change in accordance with a variable