.. What's the difference between the Amateur and Master games?

It's basically the same as the old Junior and Senior games; the Amateurs get easier puzzles and the in-game hint line on their phones, as well as a detailed task list so they can keep track of the problems they haven't yet solved. Masters get harder puzzles and no hint line, though they do now get a basic task list with the game's major goals. It'll help keep you aimed in the right direction, but getting there is up to you.