Cut is about how the diamond interacts with light
Three different things get called cut, and separating them helps. Shape is the outline of the stone seen face up — round, oval, pear, emerald. Cutting style is the arrangement of the facets within that outline. Cut quality is a third thing again: the proportions and facet arrangement that affect how the diamond interacts with light. That shows as brightness, the light the diamond returns; fire, light split into the colours of the spectrum; and scintillation, the sparkle and the pattern of light and dark areas as the stone moves.
Polish and symmetry relate to craftsmanship. GIA grades both separately, and for standard round brilliants they are also among the components used in the overall cut grade.
Cut has a strong effect on how a diamond looks face-up. For a standard round brilliant, a poor cut can make the diamond look dull even when its colour and clarity grades are high. Which of the four matters most to you still depends on what you value.
One boundary to keep in mind: GIA currently assigns an overall cut grade (opens in a new tab) only to standard round brilliant diamonds in the D-to-Z colour range.
Colour is about how little you see
GIA's colour scale (opens in a new tab) runs from D to Z. D is colourless; colour increases towards Z, which is light yellow or brown. Fancy-colour diamonds, such as pinks and blues, lie outside that range.
Many of these colour distinctions are too subtle for an untrained eye to see. If you are comparing stones, look at them side by side under the same light, and decide for yourself how much a difference matters to you.
Clarity covers inclusions and blemishes
Diamonds often have clarity characteristics of two kinds. Inclusions are internal clarity characteristics; blemishes are surface characteristics. A diamond in which a skilled grader sees neither at 10× magnification is graded Flawless on GIA's clarity scale (opens in a new tab), and Flawless diamonds are rare.
A clarity grade is not a headcount. It reflects the size, nature (what kind they are), position, relief (how much they stand out) and number of these characteristics, as a skilled grader sees them at 10× magnification.
Many inclusions and blemishes are not visible to the naked eye. Whether you can see anything yourself, at normal distance, is a real consideration when you are choosing — but it is a separate question from the grade, and it does not stand in for it.
Carat is weight, not size
Carat measures weight, not size: GIA puts one metric carat at 0.2 grams (opens in a new tab), or 200 milligrams. Carat weight alone does not tell you how large a diamond will look face-up. In a round brilliant that is cut too deep, for example, more of the weight can sit below the face-up outline, so the extra weight does not necessarily add visible size.
Cut
How proportions and facets affect brightness, fire and scintillation.
Colour
From D, colourless, towards Z; many colour distinctions are subtle.
Clarity
Inclusions in the stone, blemishes on its surface — many are not visible to the naked eye.
Carat
Weight, not visible size — and not the whole story.
How they fit together
The four describe different characteristics, not a single score. They do not tell you which characteristic should matter most to you, and different people weigh the four differently.
The useful question is not which grades are highest, but which combination looks right to you and suits how the piece will be worn.