Sugar is a simple carbohydrate obtained from sugar cane or sugar beets and is used to sweeten a cocktail.
Granulated sugar / white sugar
Granulated sugar is beet or cane sugar which has been processed, allowed to crystallize, and then dried so that the crystals do not clump together. Many people think of granulated sugar when they hear the word “sugar,” and this form of sugar is readily available in most markets. Recipes which call for sugar without specifying the type of sugar usually mean granulated sugar.
Heavy granular sugar is sometimes used to rim the glass of a cocktail.
Confectioner's sugar / powdered sugar
A number of desserts and sweets are not complete without a final dusting of confectioner's sugar, also known as "powdered sugar" or "icing sugar". Confectioner's sugar is actually granulated sugar which has been mechanically ground into a very fine powder. This powdered form of sugar is commonly used to make cake frostings, sugar glazes, dessert sauces and decorative icings. Confectioner's sugar is also used to provide additional sweetness to fried donuts, funnel cakes and beignets.
Caster sugar / superfine sugar
Caster sugar is superfine sugar, favored for sweetening drinks. Caster sugar is the name of a very fine sugar in Britain, so named because the grains are small enough to fit though a sugar "caster" or sprinkler. It is sold as "superfine" sugar in the United States.
Because of its fineness, it dissolves more quickly than regular white sugar, and so is especially useful in cold liquids. It is not as fine as confectioner’s sugar, which has been crushed mechanically (and often mixed with a little starch to keep it from clumping).
If you don’t have any caster sugar on hand, you can make your own by grinding granulated sugar for a couple of minutes in a food processor (this also produces sugar dust, so let it settle for a few moments before opening the food processor).
Brown sugar is an unrefined or partially refined soft sugar consisting of sugar crystals combined with molasses. Brown sugar is produced similarly to white sugar, with two exceptions. Its crystals are left much smaller than for white sugar, and the syrup or molasses is not washed off completely. Brown sugar contains from 3.5% molasses (light brown sugar) to 6.5% molasses (dark brown sugar).
While "white" sugar tastes the same regardless of source, brown sugar from different sources can have different flavour profiles and are used differently in different applications.