Does “coated aluminium” mean the same as “powder coated aluminium”?

Not necessarily, no. Extruded aluminium can be finished in a number of ways, including painting, anodising and powder coating. Painting is (we hope!) fairly self-explanatory; anodising involves creating a layer of oxide on the aluminium profile using an electric current and an acid bath; powder coating involves applying a layer of thermo-setting powder that flows into a smooth, hard-wearing layer on top of the substrate. So depending on the context, no: coated aluminium may not always mean powder coated aluminium.