The Clown Prince of Crime
Super Freak
Is it the same story as in the animated films?
Yeah, but they made some changes. In the comic, Two-Face's resurgence and bombing attempt occurred after the Joker emerged from his catatonia due to news reports of Batman defeating the Mutant Leader. In the film, it took place before the Mutant Leader was defeated. Because of this, Joker was not involved in Two-Face's plot at all, and it is implied in the film that Two-Face simply lied about not blowing up his men in order to ensure he committed suicide rather than the bombs being sabotaged by the Joker.
There are other minor changes and things that were cut from the film, like The Joker killing a bunch of children with cotton candy. But the overall story is the same and some things are better in the film, like the lack of news reporters talking.