A mirror is just a surface that reflects light, and white is just all colours mixed together, so a white surface is just one that reflects all light. So why is one monochrome whilst the other is a reflection?
In: Physics
Any single coloured surface reflects ONLY that colour. And the texture of the surface actually absorbs other colours.
A white MATT surface (a rough surface) will actively block red, blue, green individual sources of colours from mixing and reflecting. But add enough FOCUSED light and a white surface will act as a mirror. (See camera obscura).
A white ENAMEL (a sheen surface) will allow more colours through to reflect (hence why you can see reflections in very shiny car paints).
By using sandpaper on an enamel finish you reduce its reflectivity as more light is absorbed in the rough texture.
A mirror is a very, very flat, silver paint on clear well polished (no bumps) glass that allows almost all visible light through at any focus.
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