"Bingo the Clown," particularly with that capitalized C, sounds like the clown's stage name. The capitalization means that the word "clown" is part of the name. The form "A the B" carries echoes of the time centuries ago when people were known by their professions or other actual descriptions, and the definite article was used; "John the Carpenter," "Richard the son of William," "Daniel the Smith." Over time these evolved into the first name-surname form: John Carpenter, Richard Williamson, Daniel Smith. "The clown Bingo" or "the clown, Bingo" means that the clown's name is simply Bingo. We are talking about a clown and giving you the clown's name at the same time. In the U.S. there was a (series of, actually) clowns named "Bozo the Clown." There was a circus clown named "Coco the Clown." These would be referred to as "X, the Clown." The clown, Emmett Kelly, was a major attraction with the Ringling Brothers Circus for decades. He is not called "Kelly the Clown" because that was not his stage name. The character he played was "Weary Willie," but I'm not sure many people knew that. In any case, you would either refer to him as "Emmett Kelly" or, if necessary in context, "the clown, Emmett Kelly," never "Kelly the Clown."

They are two different ways of making reference to "a clown whose name is Bingo". For example: (1) "Bingo the clown was well known for his amusing routine" (2) "The clown, Bingo, was well known for his amusing routine" Notice I've used commas in sentence (2) to parenthesise the clown's name, but you could legitimately leave out both commas if you wanted to.

They are the same.