equanimous vs self-possessed

equanimous and self-possessed both are adjectives.

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

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

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

equanimous (adjective)	self-possessed (adjective)
in full control of your faculties	in full control of your faculties