Additional info on the differences, from Wikipedia :

This product is different from Diet Coke because of the sweeteners it uses (Diet Coke only uses aspartame), and because, unlike Diet Coke, this product is based on the original Coca-Cola formula. Diet Coke was an entirely new formula which would eventually become the basis for the controversial New Coke.

Also, Coca-Cola Zero is not a new product. The same blend of aspartame and acesulfame potassium along with the Coca-Cola Classic formula has been available for quite some time in many European countries and is commonly called Coca-Cola Light.