assertion vs say-so

assertion and say-so both are nouns.

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

As nouns, say-so is a hyponym of assertion; that is, say-so is a word with a more specific, narrower meaning than assertion:

assertion (noun)	say-so (noun)
a declaration that is made emphatically (as if no supporting evidence were necessary)	the power or right to give orders or make decisions
the act of affirming or asserting or stating something	an authoritative declaration
	one chap's arbitrary assertion