White Table Sugar mostly comes from sugar beets and is known as Surcrose. It's suppose to give your beer off flavors, or even a cidery taste if you use it to prime your beers for bottling.
Corn Sugar is Dextros, and is using for priming in many brew recipies. Normally does not cause any off flavors or make the brew cidery. The rule of thumb is generally 3/4 cups or 4 ounces of corn sugar to 5 gallons of brew for priming.
Using DME, you have to increase the amount to about 1 1/4 cups for priming, and it will give you a more malty flavor, and suppose to give you better heads on your beers, but will take 1 to 2 weeks extra to carbonate the beer.
I've actually tried light brown sugar on one of my ales and it worked great with no off flavors or cidery taste, and it took the same amount of time to carbonate as corn sugar.