pessimism vs despair

pessimism and despair both are nouns.

Word	Noun	Adjective	Verb	Adverb
pessimism	Yes	No	No	No
despair	Yes	No	Yes	No

As nouns, despair is a hypernym of pessimism; that is, despair is a word with a broader meaning than pessimism:

pessimism: the feeling that things will turn out badly
despair: the feeling that everything is wrong and nothing will turn out well

pessimism (noun)	despair (noun)
a general disposition to look on the dark side and to expect the worst in all things	the feeling that everything is wrong and nothing will turn out well
the feeling that things will turn out badly	a state in which all hope is lost or absent

pessimism (verb)	despair (verb)
	abandon hope; give up hope; lose heart