saw vs saying

saw and saying both are nouns.

Word	Noun	Adjective	Verb	Adverb
saw	Yes	No	Yes	No
saying	Yes	No	No	No

As nouns, saying is a hypernym of saw; that is, saying is a word with a broader meaning than saw:

saw: a condensed but memorable saying embodying some important fact of experience that is taken as true by many people
saying: a word or phrase that particular people use in particular situations

Other hypernyms of saw include expression, locution.

saw (noun)	saying (noun)
hand tool having a toothed blade for cutting	a word or phrase that particular people use in particular situations
a power tool for cutting wood
a condensed but memorable saying embodying some important fact of experience that is taken as true by many people

saw (verb)	saying (verb)
cut with a saw