vary vs branch out

vary and branch out both are verbs.

Word	Noun	Adjective	Verb	Adverb
vary	No	No	Yes	No
branch out	No	No	Yes	No

As verbs, branch out is a hyponym of vary; that is, branch out is a word with a more specific, narrower meaning than vary:

vary: become different in some particular way, without permanently losing one's or its former characteristics or essence
branch out: vary in order to spread risk or to expand

vary (verb)	branch out (verb)
become different in some particular way, without permanently losing one's or its former characteristics or essence	vary in order to spread risk or to expand
make something more diverse and varied
be at variance with; be out of line with
be subject to change in accordance with a variable