The only difference is that beet sugar is made from sugar beets, and cane sugar from sugar cane; however, they are chemically identical, each with a composition of 100% saccharose (sucrose). The sugar manufacturing processes are also nearly identical, although there are some small variations due to the differences between beets and sugar cane.
Beet sugar is mainly used in Northern Europe, whereas cane sugar is used in the rest of the world. To distinguish between beet and cane sugar in Europe, 1-3% of molasses are often added to white cane sugar to give it a brownish colour.