Demerah sugar is like "raw sugar". Brown Sugar is regular white sugar with molasses added back. Demerah sugar is sugar before it has been refined to white sugar. So, you can consider it "natural" brown sugar.
Brown vs White sugar: Brown may impart a caramel taste.
Table Sugar is Sucrose. Sucrose is metabolized into Glucose and Fructose. Fructose is then metabolized into Glucose. Glucose is then metabolized into alcohol. Note: Dextrose is the form of Glucose that living organisms use.
Some LHBS sell Dextrose so the Yeast have less work to do. I have no idea if that makes any difference.
Table sugar comes is two forms: Cane and Beet sugar. Bakers swear by Cane sugar. I have never read anything about differences for beer or wine making purposes.