The colours (brightness) of A and B are the same!
The reason why one sees them as difference is surprisingly easy to explain. Nature designed our eyesight to interpret the real world as models that help us to survive, and it is safer to assume that the shading on B has made a surface lighter than its surrounding squares darker, so square A (actually the same shade as B) must be rendered in our minds to be darker than B. In finding prey or, even more critically, in avoiding predation, this interpretation is safer than accurately showing the squares as the same colour or illumination.
Before you get worried, this does not happen when multiple colours or shades exist, which is much more common in the world. In a shady, dark environment, showing two identically illuminated squares as differently lit actually makes both more visible!
Who knows? If our vision was accurate in shade analysis, we might not be here as a species....
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