A grey card is meant to exhibit the correct shade of gray (18 percent I think), which should fall exactly at the midpoint of your spectrum (or your histogram if you are reading a histogram of the exposure). If you are doing a custom white balance setting on the camera, one of the ways to do this is to take a picture of a gray card. Taking into account whatever light is present, the camera will adjust white balance to make that picture match what it sees.
I would not trust a display of a gray card because any mis-calibration of the display will change it.
You use a gray card when you want to get the most accurate tonal range possible. Whether this always corresponds with the most pleasing tonal range varies, but if you calibrate exposure to a gray card then whatever dynamic range your camera is capable of will be centered, and clipping of shadows and highlights will be minimized.
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I would not trust a display of a gray card because any mis-calibration of the display will change it.
You use a gray card when you want to get the most accurate tonal range possible. Whether this always corresponds with the most pleasing tonal range varies, but if you calibrate exposure to a gray card then whatever dynamic range your camera is capable of will be centered, and clipping of shadows and highlights will be minimized.