It appears that there are several likely issues that have occurred to discolor your pool plaster.
First, from the pictures, I believe that the plaster has what is known as white soft spots (also called "spot etching") that developed from improper plastering workmanship. They show up a few months after the plastering is completed. Unfortunately, nothing can be done to rectify those white spots, and your plaster is beyond the warranty.
Second, as other TFP members have stated, it also appears that there are calcium scale deposits, which are the gray/blackish stains. Those might be able to be removed by either sanding or an acid wash, or perhaps an acid bath (Zero alkalinity) treatment. But it depends on how severe and how long they have existed in your pool.
Third, since the pool is also six years old, it is possible that those blackish stains could also be copper oxide stains. I think I read somewhere on one of your comments that some dark stains disappeared and then reappeared. If that is true, it is possible that blue/green copper stains can turn "blackish" and then disappear or return to the blue/green or turquoise color. That can happen due to extreme high chlorine levels. Pouring bleach into a pool can result in the chlorine to sink to the bottom of the pool and oxidize the blue/green copper stains and turn them blackish. But this is just a guess on what the dark grey and black stains are. A water analysis can determine whether the water contains too much copper.
Again, it is more likely that they are calcium stains. One way to tell is by touch. Blackish copper stains would be fairly smooth, while calcium deposits should be fairly course and rough like sandpaper. Calcium deposits are white to begin with, but then eventually pick up dirt and other minerals and turn to dark discoloration stains.
Lastly, some gray discolorations can be also from improper plastering. But they are very smooth to the touch, and very grayish, not blackish. Those also cannot be rectified without damaging the plaster surface. The above link given to you briefly explains those new plaster issues. I have posted two older articles on "white spotting" and "gray mottling discoloration" if you wish to understand more about those two new plaster issues.