A mirror is obviously a surface which absorbs very little of the light hitting it and bounces it back in all directions. So, by any reasonable definition, a mirror is white. But it doesn't look the same as normal white objects obviously. The reason for this is that there are actually two ways a surface can reflect light: Specular reflection and scattered reflection.
In specular reflection, every beam of light is bounced back perfectly at the same angle it came in. If a beam of light hits a surface at 60 degrees, it bounces out at sixty degrees. This is sort of "perfect" reflection and this is what's happening when we look at a mirror. In scattered reflection, the surface of the object isn't as smooth, so the beams of light do get reflected back at their original angle, but they get scattered in lots of different directions because the surface is jagged. This means we get all the beams of light coming out, but they are mixing with each other, crossing over and the original "image" is lost. This is what a white object is doing.
So a mirror is, in one sense, a perfectly smooth white surface, while a white object is a rough or jagged white surface (compared to the mirror of course). Perhaps we might want to say that a mirror is "mirror coloured" to describe "white specular".