Implicitly, training and practice are basically the same thing. It's the idea of reinforcing skills through repetition.
However, at least for me, and several others I know, the difference is more of a mindset. Practice, for me, implies target practice. It means I'm going to the range, I'm going to set up a target, and shoot at it a whole bunch.
Training, on the other hand, is working multiple skills, both alone and together. Transitioning between target, drawing, point shooting, weak hand and one handed shooting, reloads, malfunction clearing, etc.
I realize that my definition isn't completely correct, but it's how I personally look at things. Practice is fine if I just want to have fun shooting at stuff. But training is what I do if I want to get better.
Really, it's a matter of semantics. I'm well aware that they are similar in function, but for me it's a matter of mindset and content.