There are three reasons:

Color calibration

As we all know, calibrating your monitor is a key part of any digital artist work flow. The problem is, camera LCD can’t be calibrated easily (need a custom picture style) so differences in colors are to be expected to some degree.

Camera LCD are cheap

Even if you managed to balance your LCD with your screen, you would still end up with some differences because the camera LCD cannot reproduce the same color gamut as your computer LCD. This difference is subtle but it is there.

Picture Style

Finally, and this is probably the most prevalent element: images shown on the camera back are processed JPEGs using the camera currently selected picture style. Even if you are shooting RAW, the image appearing at the camera back will be a processed JPG. This is why it is suggested to change picture style depending of what you are shooting, even when shooting RAW, since it gives you better idea of your end result.

This is especially problematic when you are intershooting video clips and pictures since you are probably leaving the picture style to the Technicolor cinestyle which dulls everything.

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