tongue twister vs saying

tongue twister and saying both are nouns.

Word	Noun	Adjective	Verb	Adverb
tongue twister	Yes	No	No	No
saying	Yes	No	No	No

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

tongue twister: an expression that is difficult to articulate clearly
saying: a word or phrase that particular people use in particular situations

Other hypernyms of tongue twister include expression, locution.

tongue twister (noun)	saying (noun)
an expression that is difficult to articulate clearly	a word or phrase that particular people use in particular situations