In some countries it is a legal requirement for the camera to make a sound. There are too many people taking surreptitious pictures. Screenshots have the sound because it's helpful in letting you know the screen was actually captured.The only way to turn it off would be to turn off or lower the system sounds. Assuming you want the other system sounds, you can also set a routine to turn off the sound when you open the camera app. It will run automatically when you open the camera and return your volume levels back to normal when you close it. No user input necessary after initially setting up the routine. This will not work for screenshots, however, as the camera is not involved and there is no separate screenshot app.
