In this episode, Krusty the Clown apparently wears makeup. However, in a later episode, Krusty implies that his bypass surgery resulted in his face being permanently bleached so that it only looked like he was wearing makeup.
This short proves that Krusty was originally going to be Homer in a clown costume, but they changed that.
That being said, Bart's exchange with Krusty is eerily similar to that of the scene in "Simpsons Roasting on an Open Fire" where he talks with Homer working as a mall Santa. Both scenes have Bart finding out that his father is impersonating an icon loved by children, have Bart say his disrespectful catchphrase of "I'm Bart Simpson, who the hell are you?", and Homer respond by saying "Why, you little..." and strangling Bart.