As shilsen points out, they were one and the same in the Burton movie. This is, however, purely an invention of that movie. BB returns to the classic lore of Joe Chill, random street thug, killing Wayne's parents. The Joker was a two-bit mystery-man villian wearing a red cape who fell in a vat of magic acid that turned him into his 'happier' self. Alan Moore once did a story of it from Jack Napier (i.e. the Joker's) perspective. It was very good.
As for the Dark Knight Returns....it's still good, but hasn't aged as well as it might. Some of the 80s references feel very dated now, for example. However, WB has animated part of the DKR in the Animated Series. It was the episode where three kids tell stories about Bats, and the first is a Bill Finger story, the second is a the battle with the gang boss in DKR and I can't honestly recall the third (though I seem to recall Neal Adams linkage). Besides which, DKR is a pretty lousy place to restart a movie franchise...especially as it features a Superman who's a puppet of the government, which kills two franchises with one stroke...and requires the audience to know who Green Arrow is, for that matter.