AKA: table sugar, white sugar or regular sugar made either of beet sugar or cane sugar, a highly refined, multi-purpose sugar

a superfine granulated white sugar, dissolve much quicker than standard granulated white sugar. Ideal for making meringues, syrups, and cocktails

AKA: powdered sugar, confectioner’s sugar a type of white sugar that has been ground into a fine powder. Often with a small amount of corn-starch to prevent clumping. Dissolves easily in liquid. Ideal for icing, frosting and decoration.

AKA: nib sugar or hail sugar a coarse, hard texture with an opaque colour. Doesn’t melt when exposed to high temperatures. Commonly used in Scandinavian baking to decorate pastries, cookies, and buns.

AKA: square sugar, lump square sugar a refined sugar which has been pressed or cast into a particular shape.

AKA: sugar candy, rock sugar or crystal sugar large sugar crystals. Eaten as candy or to dissolve in tea. Can be different colours.

Sanding sugar is used mainly for decorating. Large crystals, fairly resistant to heat, adds extra texture. You can find sanding sugar in many colours.

refined white sugar with a small amount of molasses added. A wet, sandy texture and a delicate caramel flavour. Used for baked goods and savoury dishes.

refined white sugar with more molasses added in. A stronger, more intense flavour. Light and dark brown sugar can be used interchangeably.

Golden syrup (or light treacle) is a form of inverted sugar syrup. It is made by the process of refining sugar cane or sugar beet juice into sugar, or by treatment of a sugar solution with acid. The consistency is similar to honey, and can be used as a substitute for honey.
More on syrup and molasses here.