say-so vs affirmation

say-so and affirmation both are nouns.

Word	Noun	Adjective	Verb	Adverb
say-so	Yes	No	No	No
affirmation	Yes	No	No	No

As nouns, affirmation is a hypernym of say-so; that is, affirmation is a word with a broader meaning than say-so:

Other hypernyms of say-so include assertion, statement.

say-so (noun)	affirmation (noun)
the power or right to give orders or make decisions	a judgment by a higher court that the judgment of a lower court was correct and should stand
an authoritative declaration	a statement asserting the existence or the truth of something
one chap's arbitrary assertion	(religion) a solemn declaration that serves the same purpose as an oath (if an oath is objectionable to the person on religious or ethical grounds)
	the act of affirming or asserting or stating something