separate vs distinguish

separate is a noun but distinguish is not a noun.

Word	Noun	Adjective	Verb	Adverb
separate	Yes	Yes	Yes	No
distinguish	No	No	Yes	No

As verbs, separate and distinguish are synonyms defined as:

Other synonyms of separate include differentiate, secern, secernate, severalise, severalize, tell, tell apart.

As verbs, distinguish is a hypernym of separate; that is, distinguish is a word with a broader meaning than separate:

Other hypernyms of separate include differentiate, secern, secernate, separate, severalise, severalize, tell, tell apart.

separate (noun)	distinguish (noun)
a garment that can be purchased separately and worn in combinations with other garments
a separately printed article that originally appeared in a larger publication

separate (adjective)	distinguish (adjective)
independent; not united or joint
standing apart; not attached to or supported by anything
separated according to race, sex, class, or religion
have the connection undone; having become separate

separate (verb)	distinguish (verb)
become separated into pieces or fragments	mark as different
divide into two or more branches so as to form a fork	identify as in botany or biology, for example
arrange or order by classes or categories	be a distinctive feature, attribute, or trait; sometimes in a very positive sense
mark as different	make conspicuous or noteworthy
move or break apart	detect with the senses
force, take, or pull apart
divide into components or constituents
go one's own way; move apart
make a division or separation
treat differently on the basis of sex or race
separate into parts or portions
discontinue an association or relation; go different ways
act as a barrier between; stand between