What's the difference between alpha and beta glucose? 

"Glucose, C6H12O6 a monosaccharide (or simple sugar), is the most important carbohydrate in biology. Cell use it as a source of energy and is a metabolic intermediate. In addition glucose is one of the main products of photosynthesis and starts cellular respiration in both prokaryotes and eukaryotes.

Two isomers of the aldohexose sugars are known as glucose,of which only one (D-glucose) is biologically active.The mirror-image of the D-glucose , L-glucose, cannot be used by cells. In solutions, the open-chain form of glucose (either 'D-' or 'L-') exists in equilibrium with several cyclic isomers, each containing a ring of carbons closed by one oxygen atom.

The D-glucose can exist in two forms alpha-D-glucose and beta-D-glucose. They differ only in the direction that -H and -OH groups point on carbon 1 (See the jmol images below). When alpha-glucose molecules are joined chemically to form a polymer starch is formed. When beta-glucose molecules are joined to form a polymer cellulose is formed.

Glucose 3D Molecular Structures using Jsmol

When a glucopyranose molecule is drawn in the Haworth projection, the designation 'a-' means that the hydroxyl group attached to C-1 and the -CH2OH group at C-5 lies on opposite sides of the ring's plane (a trans arrangement), while 'ß-' means that they are on the same side of the plane (a cis arrangement). See below.

Haworth projection of a--D- Glucopyranose

Haworth projection of ß-D- Glucopyranose

What's the difference between starch and cellulose? 

When alpha-glucose molecules are joined chemically to form a polymer starch is formed. When beta-glucose molecules are joined to form a polymer cellulose is formed.

2-D images are all courtesy of Wikipedia.