And recently there has been the phenomenon where companies try to hide things by using confusing nomenclature. E.g., "evaporated cane juice" in products with "no added sugar." [foodnavigator-usa.com] Yeah -- "cane juice" -- it must be good for you, since they call it "juice"! Well, it's just another form of sugar... processed slightly differently, but still basically sucrose.
You need to stop confusing "ingredient list" with "chemical composition." As an ingredient, "sugar" means "refined sugar," but there's sugar in everything. Even beef is 1-2% sugar.
Most people are interested in "sugar" in the sense of "refined sugar" so-called empty calories that contain no additional micronutrients and have high glycemic index. When you refine sugar out of cane juice, or beets, or just about anything, you preferentially select sucrose from all the other sugars, proteins, and minerals in the extract.
Most food is a mixture. If your recipe is bitter, you can make it more pleasant by adding refined sugar, honey, maple syrup, apple juice, cane juice, or a host of other things. Some of those ingredients have their own distinctive flavor, which may mix well or badly with your other ingredients. Refined sugar is popular because it's pretty flavor neutral and stores forever. Cane juice is also pretty flavor neutral and cheap, but not as easy to store or transport.
An ingredient list is not a chemical analysis