You will need to play with this to achieve the desired result. Think of the brightness applying to the image if it is black and white only and the intensity as applying to colors only. In reality, white is comprised of all the colors so this isn't really a true statement but should help you decide which function to use and when. Contrast and Saturation achieve a different role in image processing. Just as mentioned above where brightness is primarily a black and white function, contrast is also.
Saturation is a color function just as intensity was above.
What is generally desired is a smooth transition from black to white through each individual color as well as the grays. These are the functions used to adjust images which may require either an increase or decrease in the graduations. The gamma curves above did most of the work already however, there are times when an image needs a little help in this area. If a photograph was shot in bright light and is over exposed, the ability to resolve features in faces or textures in fabrics may be lost. In other cases, the photo was taken in a shadow of a building or other object and the detail is also lost due to sharp transitions from light to dark.