self-possessed vs self-contained

self-possessed and self-contained both are adjectives.

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

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

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

self-possessed (adjective)	self-contained (adjective)
in full control of your faculties	constituting a complete and independent unit in and of itself
	in full control of your faculties