twisting vs twisty

twisting is a noun but twisty is not a noun.

Word	Noun	Adjective	Verb	Adverb
twisting	Yes	Yes	No	No
twisty	No	Yes	No	No

As adjectives, twisting and twisty are synonyms defined as:

Other synonyms of twisting include tortuous, voluminous, winding.

twisting (noun)	twisty (noun)
the act of distorting something so it seems to mean something it was not intended to mean
the act of rotating rapidly

twisting (adjective)	twisty (adjective)
marked by repeated turns and bends	marked by repeated turns and bends