Why is puzzle rating much higher then rapid and blitz rating for most people?

The puzzle has three things that make it much easier than other ratings. First, it's only one move usually, then you know the rest. It's not like a full game where you will make a mistake or blunder. Second, you can repeat the puzzles, and so it's like doing it over. You can't redo a game. Third, you know ahead of time it's going to be a mate. In a game, you don't know if you are down or ahead usually in 2 point evaluation or less games. So, you are more likely to miss the mates because you still think you need to get an advantage you already have. That opens up the possibility for mistakes and blunders.