Technically, Keaton and Kilmer and Clooney are all the "same" Batman, too...but Clooney shows up in the last scene. It's all a big bunch of nonsense, really. Just make it however you want it to be in your head. There's no right answer.
I'm also on the record as really liking this movie. I thought it was so much fun, and I really loved how the end just twisted into the sadness of inevitability. "Young" Barry gets corrupted and turned into something so dark and "wrong" cause he just can't accept the basic lesson of life...that growing up sucks and we all die. That life lesson along with all the repeated deaths of Keaton and Supergirl....it's some dark **** man!
I have no idea what the "original" idea for this movie was supposed to be, but I really liked what they cobbled together and presented in the end. It worked for me. It's too bad more people didn't give it a chance.