When a label on a food product reads "sugar" it means sucrose. Whether its cane or beet sourced it doesn't matter. Any other sweetner, ie. dextrose, fructose, invert, etc., must be identified by its true name. If the bag in the supermarket says "cane", it is from sugar cane. If "cane" is not on the bag it is most likely beet although there may be a situation (rare) where the prosessor is sourcing from both types and may even blend (again rare). Both cane and beet sugar (sucrose) rate 100 on the sweetness scale for sweetners.
Chemically cane & beet are the same but... I have found that beet tends to "feel" damp and many times has an odor associated with it that you do not ever notice with cane. Beet has been known to possibly be the cause of peculiar issues especially with baked products.
Beet is cheaper; that's why large manufacturers use it. Do yourself a favor and use cane. You just might avoid a peculiar issue.