The primary difference between Standard and Premium color books is the paper stock the books are printed on.
Standard Color uses thinner paper and does not hold the color ink quite as well as the thicker, premium, paper does. This means the colors won't be as sharp or bright as a Premium book.
The Premium color uses a thicker paper that can hold heavier ink saturation and thus the color pages look a little brighter and the contrast is much more powerful. Premium is more expensive to produce in part because of the heavier paper and there is more ink used in the process.
Standard color books are printed on 50-lb. standard white paper. Premium color books are printed on 70-lb. white paper.
Examples of each can be found here: