The comics universes are pretty complex. They can even have different timelines within the comic, for example Teen Titans have Earth 52 and New Earth, to name just a few (can't remember, but there's a shitload of more). I don't know about Marvel but DC tends to mix and change incidents as they see fit, and sometimes the same heroes can have completely different origins only because they are present in several timelines.
With cartoons and movies based on the comics, they are usually just adaptations. Unless the studios (DC, Marvel) officially state that "hey, this shit is canon, don't hate on it", but then they mess with it themselves by making another timeline and changing the facts.
At least that's my experience with DC

I've never gotten involved with Marvel characters to dig up the comics facts about them :)
So to refer to your doubts, Batman movies are probably just loosely based on the comics and are their own thing, then the same goes for Batman cartoons and are probably seperate from the movies. As I said, to me they seem like different views on the same thing ;)
Also, DC tends to avoid repeating the same character in different shows. for example they made this new show Titans, adaptation of Teen Titans, and excluded the character of Cyborg from it, because (I believe) he is present in the Justice League franchise, even though Cyborg was one of the original Titans.
I elaborated too much ;_______;