It is said that white color reflects all the colors of white light. Silver also reflects all the colors of light. Then what is the difference between silver & white? Also why is it so that we can see our shape in silver (like mirror) and not on smooth white colored surface?

Depends what you mean by silver. To me silver is just a greyish color - reflects them all with some loss - a dull white if you want.

But the thing with the silvered surface of the mirror is that it's finely polished.

White color is not polished - if it was, then it would be silver like a mirror!

A mirror reflects specularly, white reflects diffusely. (click the links).

If you have any more trouble understanding, please come back and reply!

In a finely polished car, it's actually a layer of buffing wax that reflects specularly (like water), and the paint reflects diffusely, which is why you can see both the color and your reflection.