Carbohydrate configurations
There are 32 isomers of C6H12O6, of which you have named 6. The most common one is D-glucose (dextrose). I don't think all of the 16 L-saccharides are found in nature.

α and β refer to the connection between rings, whether the ketal (or aldehyde) oxygen is axial or equatorial.

  Structures made with ChemDraw.