I use Bon Ami to scrub my All Clad stainless steel pots and pans when they need it (a soapy dish brush is usually fine to get off most leftover food).
When I’m left with spots like these (see pics) after I’ve washed them well, I use a few tablespoons of white vinegar and rub that in vigorously and well, in every direction with a small piece of paper towel. Pour that vinegar in the next pan to remove spots, rinse the original pan and dry. All your spots will be gone in seconds.
DON’T DISCARD that vinegar. You can put it in a little dropper bottle (I use empty, cleaned out Aveda sample size shampoo containers) and use two or three drops of that vinegar on an especially intractable weed in your yard/garden! Don’t give in to that more is better “philosophy” and use too much. You don’t want to kill beneficial microbes in the soil or otherwise change your soil’s acidity. Cut the weed down to the dirt and apply literally (like literally “literally”) two to three drops of vinegar on the cut part (better if it’s down into a hollow stem).