First, don't confuse diamond "cut" with "shape." Shape refers to the general outward appearance of the diamond, (such as round, emerald, or pear). When a diamond jeweler (or a diamond certificate) says "cut," that's a reference to the diamond's reflective qualities, not the shape (or at least it should be, we have found that even some "jewelers" don't appear to know the difference between "cut" and "shape").
The quality of the "cut" does make a difference in how a diamond looks.
Diamond cut is perhaps the most important of the four Cs, so it is important to understand how this quality affects the properties and values of a diamond. A good cut gives a diamond its brilliance, which is that brightness that seems to come from the very heart of a diamond. The angles and finish of any diamond are what determine its ability to handle light, which leads to brilliance.