This common "table" sugar is (like all sugar) refined from sugar cane or beets; in taste tests, cane and beet sugars were indistinguishable from each other. The relatively fine crystals and neutral flavor make this sugar the most versatile sweetening agent.
Brown Sugar is white sugar with molasses added for flavor and extra moisture. Dark brown sugar simply contains more molasses than light brown sugar; we find the two types of brown sugar are interchangeable unless specified by a recipe.
In addition to imparting a caramel flavor, brown sugar tends to make cookies more moist and chewy. Why? Molasses is an invert sugar. Invert sugar is especially hygroscopic, pulling water from wherever it can be found—the best source being the air. Cookies made with brown sugar tend to stay chewy because the invert sugar pulls in moisture even after the cookies cool. Note: most organic brown sugars have larger crystals than standard brown sugar. Because these large crystals don't dissolve as readily in baked goods, generally we do not recommend organic brown sugar for baking.
Sucanat is short for sucre de canne naturel. Sucanat is a natural cane sugar that is made by extracting the juice from sugar cane and then beating it with paddles to form granules. Sucanat is less processed and more natural than white sugar.