there really is sich a thong as brushed aluminum surface finish.
I use cast aluminium boxes for many of my electronics things, and I like the almost "stainless steel look" that I get if I sand the surface (320-400 grit). I assume this is what others mean when they say "brushed aluminium surface finish" (based on web image searches, they match). It does not seem to tarnish (oxidize) in normal use, not even from my sweaty and oily sausage fingers handling them.
I do also like anodized aluminium finishes with black, blue, red, or white dyes. I find the anodized un-dyed look a bit dull; you see this often in all sorts of furniture. In some ways color-anodized aluminium looks like paint, but the colors don't really fade and ordinary scratches don't have a different color, and it obviously doesn't peel off even with chemicals, so it at least feels more durable.
(And, as mentioned, anodizing does not hinder cooling properties at all, and can even help a little bit in some specific cases.)
I don't understand how anyone could mix the two.