As far as I know, both icon A and icon B mean mesh. My question is why Blender has two different icons? What's the difference?
To echo the commenters, the orange one means “object with mesh data,” where as the thinner triangle with dots at the corners means “mesh data.“ Here is the manual page for a little more on the subject. Similarly, while a curve data block is a thin line with dots at the end, an object with curve data assigned to it is shown as a thick orange line, but still in the shape of the curve data icon.