What are these stains on my stainless steel pans? I've had enough of the homemaker advice of baking soda or barkeeper's friend products - their advice isn't working.  I need a chemist!

Please see the two photos below.  This pan isn't quite as clean as I could possibly get them if I scrubbed and scrubbed with a Brillo pad, but it's close - and as clean as I can get it would only last for about one use before it needed more intense scrubbing.  

The brand of this pan is Cuisinart which is relevant only for the particular variant of stainless steel they might be known to use, but I don't think my experience with this brand is much different than I've had with, say, Calphalon stainless steel pans.

I refer to these blackened areas as stains because they have no significant dimension to them, as opposed to "baked-on-crud" which has a dimension and is more expected/accepted by me than the stains.  The stains are rougher than the shiny parts though, impacting use.




1) Why am I getting these stains?  Am I doing something wrong (heating technique or kinds of food chemicals that adhere to SS)?  Are these pans inferior and really I need to buy very high-end/expensive pans (for a different grade of stainless steel) for them to be indestructible?

2) With knowledge of the chemistry involved that leads to this visual effect on the stainless steel, is there an industrial chemical (like those in carburetor cleaner or something) that could clean this stuff off without damaging the pan and which I could completely remove (to avoid toxicity in my food)?
It could be that metals in your tap water are plating out;  i.e. the more active iron in stainless steel is being replaced by a less active metal such as copper. Manganese also tends to precipitate, leaving stain, and these, in particular, are dark colored, but can be removed.

Have your tap water tested, either at a nearby school or with a commercial kit(s) that include copper, manganese and lead tests. If there is a high concentration of anions, you might want to install an ion-exchange water softener.