Not at all. It is absolutely possible to be a bit of both, and someone of Neo's skill would be a bit of both. After all, a well rounded cracker must also be a bit of a hacker and vice-versa.
I realize the difference between the two. But there's a bit of bleed-over between the two definitions. I mean, that's like saying that someone's an Economics Major, but not a Business Major. It takes a bit of Business to know Economics.