I don't know all the chemistry of it, but stainless steels form a protective layer on the surface, by reacting with air, that protects them from rust and corrosion.
Some chemicals can destroy this layer, allowing the steel to be attacked. Acids, and for some stainless alloys, salt, can do it.
If you don't clean them off immediately, you can get deep corrosion.
As far as I can see,the only cure is to polish it off. I use a green nylon pan scourer. I fear a metal scourer would leave fine scratches.
There are metal polishes you can use with a felt polishing mop, they can take off surface tarnish but they would be very slow on deep damage. Solvol Autosol is an example, and you can get solid versions called polishing soap which are clean to use.
BTW, on "brushed finish" stainless pans or sinks, only rub in the direction of the original brushing, never in circles which will catch the light wherever you view them from. I don't think you can restore mirror finish stainless without leaving marks.