"cane sugar" is cane sugar, because sugar can come from a few sources, including cane and beet. Most of the white sugar you know is either from cane or beet and it's generally glucose. Another sugar, fructose, is fruit sugar, or grape sugar, which is dextrose - they are all "sugar".
Indicating the (near) exact type of sugar is not a bad idea.
Indicating the (near) exact type of sugar is not a bad idea.