You are looking at color correction a bit incorrectly. The point of color correction isn't to make it so that colors that are the same in two images show up exactly the same in another image taken under different conditions. The point of color correction is to ensure that images consistently appear closer to the way the scene actually was.

If there are changes in the lighting between images, there may also be differences in the way each part of the physical object should look. For example, if the image is really dark on one side and really bright on the other and you give even light, there is a high contrast. If you put lots of light on the dark side and no light on the light side however, then the image should appear very low contrast since the sides actually appeared very close to the same color under those lighting conditions.

Assuming lighting conditions are similar, the curves tool is probably the most helpful tool for color correction. You can set your white point to the white side, your black point to a black side and your white balance can be set based on the grey card. This gives you a decent starting point, however the level of response in the scene to spread information out is still key.

If there are a few highlights that make all the shadows too dark, you can use curves to pull up the middle-left section in order to brighten up the shadows while still preserving deep blacks. Similarly, if the bright parts aren't dark enough, you can pull down the middle-right parts and increase the apparent detail in the brighter portions of the image.

It isn't an exact science though and it takes a lot of practice and tweaking to get it just right. It still won't let you correct for major changes in lighting, but it can help you achieve a similar look for images that may have had differences in exposure or minor differences in lighting intensity or color. It won't change the fact that the lighting was different and the actual RGB colors are different, but it can make them look (to the human eye) like the objects are the same color in real life.