Why is shape and cut different in loose diamonds?

Every diamond is individual. Diamonds are graded on four parameters. The are popularly known as 4 Cs of diamonds: Cut, clarity, color, and carat.

The shape of diamonds can be classified on the basis of Brilliant Round, Princess Oval, Marquise, Pear, Heart, Emerald, Radiant, Cushion, & Asscher.

Cut is classified into Shallow Cut, Ideal cut and deep cut.

The cut of a diamond affects its Brilliance (reflection of light), whereas Polish (smoothness of facets) and Symmetry (alignment of facets) affect the sparkle of a diamond. A poor polish can make a diamond look dull and a poor symmetry can misdirect the light, reducing the sparkle. [contributed by a gemologist]

Another Answer

Raw diamonds are cut in order to preserve the highest carat weight, and ... and to show off the natural stone's best qualities. The raw stone may be exceptionally clear -- the clarity parameter, or of a choice colour -- the colour parameter, either 'white' or coloured. After taking these two parameters into consideration, the diamond cutter then will chose a cut -- the cut parameter, to preserve the highest carat weight possible.

About 60% of a raw diamond's total carat weight is lost in the cutting process, so finding a way to minimize this loss is critical while maximizing the stone's best feature(s).