When cleaning stainless steel does shiny not necessarily mean clean?

I guess it would depend on what you are cleaning, what it is used for, and what you consider clean. If I have a stainless steel hunting knife and I make it shiny again after it gets dirty, I might consider that clean. If I have a stainless steel glass I drink out of, I might not consider shiny to be clean. The difference has to do with surface imperfections which can harbor bacteria. Minor scratches could be enough to give bacteria a place to hide and grow. Simple wiping may not get these areas clean.

Stainless steel pots are a slightly different example. The pot is used to cook food so bacteria may be a consideration, but you are heating the pot to a point that you will kill most bacteria. That is why you “season” a cast iron fry pan and don’t have to (and shouldn’t!) scrub it down to bare metal after each use. Using the pan or pot will kill most bacteria.

Don’t use bleach, it will cause stains !

Use a paste made of baking soda and water, use soft cloth (never use Brillo or any abrasive pad) rinse with water real good.