That is only part of the difference. Type II must be sealed (contributing to corrosion resistance) whereas Type III is typically not. You can seal Type III to contribute to corrosion resistance at the sacrifice of lower abrasion resistance (the whole point of Type III). Even with full duplex sealed Type III, in practical application we've still found the best saltwater corrosion resistance with Type II Class 2 dyed ano, particularly with regard to galvanic corrosion around stainless fasteners.
Just to be clear, I always reserve the right to be wrong
It sounds like you know way more than I do about the particulars of anodizing and I appreciate the education.