slang term vs saying

slang term and saying both are nouns.

Word	Noun	Adjective	Verb	Adverb
slang term	Yes	No	No	No
saying	Yes	No	No	No

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

slang term: a word or expression that is outside of standard usage and is very informal
saying: a word or phrase that particular people use in particular situations

Other hypernyms of slang term include expression, locution.

slang term (noun)	saying (noun)
informal language consisting of words and expressions that are not considered appropriate for formal occasions; often vituperative or vulgar	a word or phrase that particular people use in particular situations
a word or expression that is outside of standard usage and is very informal