An 18% gray card that is also guaranteed to be color neutral can be used in several ways.
First, it can be used to assist in making exposure calculations by letting you measure the light falling on the subject, even though you may only have a reflected-light meter such as the one in your camera.
Second, you can use the gray card as a color (white balance) reference for doing the custom white balance like you've done with white paper. There are two BIG differences between "white" paper and the gray card, though. First, you can use the very same exposure settings with the gray card and the scene but with white paper you must use a radically different exposure setting so that the white paper is not overexposed in the custom white balance setup image.
Third, a gray card can be EXTREMELY handy to use IN THE SCENE. I always shoot in RAW mode (though I also make .JPG image files at the same time). Whenever I have a need for accurate color rendition, I will place my neutral gray card in the scene for a test shot with the same lighting as a series of shots to be made and with the exposure settings on the camera the same as for the whole series. Then, when doing RAW conversion in post-processing, I use an "eyedropper" tool to sample the gray card in the test image. The resulting color-related numbers are then transferred to the rest of the series of images in a single batch conversion. White paper could not be used for this purpose because it's likely that it would be overexposed in at least one color channel.
Finally, "white" paper is seldom truly neutral. Paper manufacturers do all sorts of things to make the paper appear bright white, etc., that actually add a bit coloration to the paper. This makes the paper less than ideal as a white balance reference.