byword vs adage

byword and adage both are nouns.

Word	Noun	Adjective	Verb	Adverb
byword	Yes	No	No	No
adage	Yes	No	No	No

As nouns, byword and adage are synonyms defined as:

byword and adage: a condensed but memorable saying embodying some important fact of experience that is taken as true by many people

Other synonyms of byword include proverb, saw.

byword (noun)	adage (noun)
a condensed but memorable saying embodying some important fact of experience that is taken as true by many people	a condensed but memorable saying embodying some important fact of experience that is taken as true by many people