HDR Paper White controls the brightness (in nits) of how bright a paper white surface should be, the rest of the scene's brightness will be calculated relative to this Paper White value. We use this as a baseline for how much light your display should be outputting and controls how bright the scene should look overall. This is useful for adjusting to different lighting conditions in your play environment.
HDR Contrast is a gamma control for the final image, it'll take the colors and increase the overall range between the brightest parts and the darkest parts of the image. The higher HDR Contrast is, the larger this difference becomes, while the lower the contrast is the more washed out the image becomes. This was more or less included to help users tune the image to their liking and what they felt looked best on their displays.
HDR Side by Side Visualizer toggles our HDR gamut expansion for the left hand side of the screen, to allow users to compare what the game would have looked like had we not used the wider color gamut of their HDR display. The difference is really noticeable on maps such as Neo Tokyo and Aquadome, which have a lot of bright and vibrant colors. This setting is more or less just for fun and to show your friends what a cool TV you have. :P
Keep in mind that TVs will do all sorts of processing after the fact, such as modifying brightness or colors (LG displays have a Dynamic Contrast option, for example), or Sharpness settings which might create a brighter image overall as a side effect of edge enhancements. If you're feeling some eye strain, try reducing HDR Paper White in order to "darken" the overall image and modifying HDR Contrast to something more pleasing.