It's the difference between how your camera and your eye/brain see the scene.
Many projectors scan each color channel in sequence very rapidly. It's too fast for our eyes to pick it up, as our brains average the sequence of each color channel. But if our camera is using a shutter time that is shorter than the refresh rate of the projector, it only sees part of the color sequence.
This is particularly true of most consumer cameras that use either a mechanical shutter that starts exposure on one side of the sensor and ends on the other or an electronic shutter that scans each line on the sensor in sequence from one side to the other (or from top to bottom). With the mechanical shutter, faster shutter times are exposed with the second curtain chasing the first curtain across the sensor. Only a narrow slit is being exposed at any one time. As the slit between the two shutter transitions the face of the sensor, the projector is flickering between each of the color channels it uses. Even with a shutter time of 1/8000 second, it still takes about 1/250-1/400 second for the slit between the two shutter curtains to transit the entire sensor. Electronic shutter is similar as each line of the sensor is read in sequence. When the last line is read then the camera starts reading at the beginning again.
The solution is to increase exposure time long enough to cover a full cycle of the projector's sequence as it goes through the color channels. In order to prevent overexposure, you may need to reduce ISO, close down the camera's aperture, or even use a neutral density filter.