As was just mentioned, there's no truly Canon creation story behind the joker. Each television series, comic series, and film series, gets to take crack at it however they want, if they even want to.
Joker in the Tim Burton movies has a certain origin. That origin is different from the joker in red Hood. And seems like it would need to be different from the Heath ledger joker. And appears to be different from the Phoenix Joker. The red Hood joker, despite being animated, clearly seems to have a different origin from the Mark Hamill joker, from an earlier animated series.
Honestly that's one of the things that I enjoy most about comic series. The ability to use the same characters to tell different stories. You can make tweaks to how characters met, or how they came to be, or how they were raised. But then you can drop them in the same suit and persona that we've seen before, and we get a new feeling a new flavor for how they got there, and potentially what they'll do now.