collected vs self-possessed

collected and self-possessed both are adjectives.

Word	Noun	Adjective	Verb	Adverb
collected	No	Yes	No	No
self-possessed	No	Yes	No	No

As adjectives, collected and self-possessed are synonyms defined as:

Other synonyms of collected include equanimous, poised, self-collected, self-contained.

collected (adjective)	self-possessed (adjective)
brought together in one place	in full control of your faculties
in full control of your faculties