No, they are not. Both are essentially the white flesh of a coconut, but both differ in texture. Desiccated coconut is the dry form of grated coconut, and is finer compared to coconut flakes. Grated coconut often comes in 2 forms, freshly grated coconut (which is moist and slightly wet) or dry desiccated coconut. In most recipes, it is important to take note of the form that is used as the dry desiccated coconut is often very light as compared to the fresh one. Hence when measured, 100g of freshly grated coconut will be a lot lesser than 100g of dry desiccated coconut. My cherry coconut cookies are made using the fresh grated version. Coconut flakes often come in long, thin strips and are sometimes sweetened. Though these are essentially dried coconut, they are not as dry as desiccated coconut.