There are about 130 pieces in the game. I don't have exact estimates for the amounts of the first two types (green and yellow; easy and medium difficulty, respectively, and used to unlock new areas and new puzzle mechanics, respectively), but I'm fairly sure there are about 20 green and 30 yellow pieces. There are exactly 49 red pieces (difficult, can be used to unlock the second ending and part of the third ending or simply collected to get the first ending), 30 stars (found all over the maps, often in hard to reach areas, and used to unlock the silver piece maps), and 9 silver pieces (difficult to very difficult, used to unlock the third ending).
Additionally, three extra stars can be acquired by redeeming reward codes from the free "Sigils of Elohim" game. You can also unlock three puzzle hints from this game in addition to the three you can get in the game, but each hint can only be used once and they can only be used in the red piece puzzles.