It's the same characters, but the whole movie is set on an alternate time line.
The whole idea of the movie was to bring back the characters we all know and love, but without the awkwardness of making the actors try to replicate the great actors of the original tv series to a t, and without trying to stick to the exact time line of events and occurrences that took place during all the movies and the tv episodes. It would have been too hard not to mess that up.
So, JJ Abrams decided to go back and mess up time a little, so that the characters would have a reason to be a little different, and there would be no need to worry about when things happened in the future. Now, he can call on anything new he wants, or anything from the past.
But all in all, the characters are pretty much the same, despite a few alterations (spock appears to be showing A LOT more emotion and is currently dating Uhura, and kirk seems to be a little more of a wild child, which may be linked to his experience growing up without a father). Oh, yeah, and there are now 2 spocks. Old original series spock (you know, just in case we need a little back-in-the-day flair) and new spock.
And, the overall story is the same, you know, the prime directive "to boldly go where no man has gone before"