Lots for Sale - this contains colors in which current part is being listed for sale.
On Wanted list - this shows which colors Bricklink members have added to their "wanted list". It doesn't mean parts in this color have existed. Most likely this being used to add non-existing color to list of wanted items and mark for notification. In such case if wanted ...
The best way to figure out what colors a set of parts have in common is to use BrickLink’s Stud.io digital design software. I am unable to show screenshots at the moment, but here are the steps:
Place the parts in question on your virtual building workspace (doesnt matter in which color)
Select all the parts together, either by:
using the ...
Unfortunately, you need to check available color for each individual part:
From what I can see most of the colors 11203 comes in are available in other parts as well.
Following your edit I can suggest another option for you - Color Guide. Select a color and click on Parts column to find all parts available in particular color.
The difference is actually explained within the naming, which comes from Bricklink, a place where people buy and sell LEGO items around the world. In cases like Bricklink, especially with AFOLs, it is necessary to know which exactly parts you are dealing with.
During the years LEGO has been upgrading parts, where Tile 2 x 2 is not an exception.