Yeah, black discoloration is just corrosion as well. It has to be polished out, and takes a little more "elbow grease" so to speak. Depending on the finish of your sword, any abrasives may alter the appearance, so you have to be careful.
With my Albions, those dark spots come right out with a grey (fine-grained) scotchbrite pad and some oil and/or rust remover. But Albion does their finishing with those same scotchbrites, so it doesn't alter the appearance to use them.