Explanation
Before I go through the examples, I want to talk about how this illusion works.
Firstly experience it with the following link:
http://web.mit.edu/persci/gaz/gaz-teaching/flash/contrast-movie.swf
Reading through many materials and seeing many of the pictures, I think the cause of this illusion is the change of average background light intensity, or illumination. With darker background (less light intensity), the grey bar seems lighter, and with lighter background, the grey bar seems darker.
The simultaneous contrast illusion does not only exist in white, grey, and black, but also in other colors. That is what makes it useful. The contrast illusion gives artist two options: to use the same color and let people perceive them as two, or to use two different colors in different backgrounds to make people perceive them as one single color to preserve the consistency.
Furthermore, the topic goes from simultaneous contrast illusion to simultaneous contrast. Every artist may use simultaneous contrast to emphasize the main part of their artworks, or use different color of background to express different feelings. We can see more in the examples I provide.