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The first link, you normalize your image coordinate in pixel to the range [-1 ; 1], the second link your normalize in order to have the normalized image plane located at the focal length=1 by dividing the 3D coordinate expressed in the camera frame by the Z coordinate (more info here for example).

The "first" normalization is not used (AFAIK) in the calibration subject, it is the second one which is used. In general, it is the second normalization which is used.