self-possessed vs equanimous

self-possessed and equanimous both are adjectives.

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

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

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

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