The definition of a Sugar that makes sense to a diabetic is-
sugar is anything that tastes sweet.
Anything that tastes sweet is going to raise blood sugar.
Even Aspartame (nutrasweet), xylitol, stevia and malitol all trigger a rise in blood Sugar of varying degree, because they work on the sweet-taste receptors on both the tongue and the gut lining. (Protip, sweet on the tongue IS sweet to the gut, the taste receptors in both places are both the same).
I've lived with type 1 diabetes many years, I'm sayin' this because of experience (and especially if you're looking for what to eat with that condition!).
Sugar fron Sugar cane is called sugar 'cuz it's sweet, the same with beet sugar, etc, etc. Plants produce similar molecules to eachother, the chemical structure of the sweet substances we refine out of them just appear subtly different under analysis.
You'll do best understanding all this by reading https://en.wikipedia.org/wiki/Sugar .
'Sugar' is the name of the big family of sweet-tasting chemicals, monosaccharides, polysaccharides, -tols and all the rest are synonyms and categorizations of relatively the same substances. Generally, sugars are simply made of carbon, hydrogen and oxygen molecules.