To me, the stains look like “dirty scale” where scale forms in a layer combined with or over top of the general dust & dirt in the pool. A chip out and re-plaster would of course fix the stains issue, as well as roughness and give you a nice, new finish. An acid wash might also fix the stains and get you a few more years of life out of the old plaster. What to do depends on what you’re trying to accomplish. Either way, for a great result, the workmanship and experience of the folks doing it is very important.