The cut does not refer to the stones shape. Instead, it refers to the symmetry of the stone and the way in which it has been cut and polished; the cut is key to a diamonds fire and brilliance. A well-cut stone will bounce the light around in an even pattern and will reflect the majority of the light back out the top of the stone. A poorly cut stone will lose light out the base and sides of the stone and therefore it will not be as firey as a well cut stone.
The proportions of a diamond refer to the ratio difference between the table size, crown angle and pavillion depth. A wide range of proportion combinations are created and these measurements will be decided when the stone is cut to get the most out of the raw diamond possible. These infinite possibilities have a knock on effect on the mm measurements of the diamond in terms of size and so this is why the carat rating is not the ideal method when choosing the size of a diamond; the visual measurements and the cut’s influence on light reflection are far more important that the weight measurement.
For more information, visit my blog post all about the 4 C’s of Diamonds