The one thing they all have in common is that they're power pitches, with little difference in speed. Now, the slider is the one I'm most familiar with, because it was my strikeout pitch for years, so let me tell you something about that one.
I learned the slider when I was sixteen. My instructor, a key member of the Yankees' Big Three pitching rotation, told me "Throw it like a curve, but roll your wrist, don't snap it." He showed me the grip he used---very much off-center, with the index and middle fingers very close together and the middle finger just touching one seam, the fourth and fifth fingers sort of curled up on one side of the ball and the thumb underneath for support. He demonstrated the wrist action, and therein lies the difference: it's a lot easier than what one uses for the curve. I threw my curve with a sharp karate-chop wrist snap, so I needed to ease up on it for the slider. I got the hang of it in about ten minutes, but I was well aware that one does not master that pitch overnight, so I spent some months working on it and refining it. It became my strikeout pitch in short order, and when I added the crossfire---oooh, is that a beautiful and lethal move that works only with the sidearm delivery---that gave the batters no end of conniption fits! (I was a natural, honest-to-gosh sidearmer.)
The cutter is a sort of variation of the fastball, and Mariano Rivera is the past master of that pitch. I'm not sure how he does it, but I think he does something with the grip just before he releases the ball. One thing for sure: I'm surprised that the batters in the rest of the league haven't deluged him with bills for replacements for all the bats he's broken with that pitch!
And there you have it. Three power pitches, each a little different but all with that one thing in common---you have to throw them with the same arm motion and the same arm speed. 8)