Anodized aluminum is pure metal that has been altered by chemicals and an electrical current. This process causes a controlled oxidation that covers the every part that has been treated. The oxide formed is harder than steel and extremely porous. Anodized aluminum is easier to dye that plain aluminum. Polished aluminum is aluminum that has been purified and polished. The metal can be polished to a high gloss or to a brushed finish. Polished aluminum is used in many of the same pieces as anodized. It takes a careful eye to distinguish the difference.
Look at the texture of the metal. Anodized aluminum has a matte finish. Highly polished aluminum is the most reflective substance on earth. It even reflects more than mirror glass. So, if the surface reflects light, it is most likely polished. However, just because the object has a matte finish, doesn't necessarily mean its anodized. Some polished aluminum has been given a brushed finish which is difficult to distinguish from a matte finish.
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Look at the color. If the piece is painted, try to scrape a small amount of paint from an unobtrusive area. If no paint chips off, then the piece has been dyed. Only anodized aluminum is porous enough to allow dye to seep into the finish.
Scrape a penny across an unobtrusive portion of the metal. Polished aluminum is very soft, as all natural aluminum remains. But, anodized aluminum has a surface strength harder than steel. If the penny is able to scratch the finish, the material is polished aluminum. If the penny leaves a streak of copper on the item, then the surface is harder than the copper and the piece has been anodized.