Diamonds can be found in every color. Different minerals and gases create the "Fancy" colors. Fancy is a true colored diamond versus a diamond that is just off color.
The cut of a diamond is different from the shape of a diamond. Cut refers to the facets, depth, and width of the diamond.
Cut is the most important "C." Too shallow and the light passes through. Too deep and the light never makes it back to the top. Clarity and Color will not make up for a poor cut.
Click the link below to watch a Gemological Institute of America video on the 4 c's of diamonds.
The graphic shows jewelers terms and what they relate to on the mounting.