How is shooting from the right different?

In moving to the right (for right handers), you will not have time to get your body all the way "opened" just so. Turn as much as you can to "sort of" get open, get the hand, ball and eye in approximate alignment, and then let the shot fly. The "letting the shot fly" idea is the key thing, trusting yourself with all that movement and letting go.

With such shots, I feel it's really important to catch the UpForce energy (leg drive) powerfully, get the ball to the Set Point quickly, get aligned as much as possible, and then make, what I call, a "full out" Release action, strongly connected to the target. The Release and Follow Through will get the ball into the basket, just so they are supported by strong lower body action, early in the jumping action for most shots. Shooting off the move adds variables, so those shots are more difficult to hit. But if you are connected to the target powerfully throughout the motion, driven by the strong muscles of the legs and middle body, and if you Release and Finish well, your performance will be as high as possible.

As you're aware, moving to the left for right-handers is easier because you're already, automatically "open" in stance. However, moving right does have the advantage of the pivoting on the left foot and stepping in to create the jumping action. That pivoting and jumping action gives the player more power than moving to the left, so they both have advantages.