Extruded aluminum is aluminum that is melted down and extruded, pushed through a certain 2d shaped hole. This can result in square tube, rectangular tube, an L shaped extrude,
… and an infinite array of other shapes. Powder coated aluminum is aluminum that could be extruded aluminum, that is cleaned, coated with a colored plastic powder, and then baked so that the plastic powder melts and forms a smooth, nice and even coat of colored plastic over the part. This is basically painting the part. Anodized aluminum is aluminum, again this could be extruded aluminum, but it couldn't be powder coated aluminum, that is put in a chemical solution, possibly sulfuric acid, and then a current is run through the aluminum. This causes a reaction to occur where a layer of aluminum oxide gathers on the surface of the part. The processes is then stop and the part can be colored if desired. Anodozing aluminum gives the part better corrosive resistance and makes the surface tougher and harder than it would have been if it had not been anodized. It does add thickness to the part which can be a downside, but it also is lighter than a powder coat if a paint job is desired. (MORE) 
