set apart vs pick out

set apart and pick out both are verbs.

Word	Noun	Adjective	Verb	Adverb
set apart	No	No	Yes	No
pick out	No	No	Yes	No

As verbs, pick out is a hypernym of set apart; that is, pick out is a word with a broader meaning than set apart:

Other hypernyms of set apart include choose, select, take.

set apart (verb)	pick out (verb)
set apart from others	pick out, select, or choose from a number of alternatives
select something or someone for a specific purpose	detect with the senses