My understanding was that there's not really any such thing as "HA-II," and that it's either HA-III or just "anodized," but that may only be some kind of semantic thing, (or I may be wrong entirely!). From my experience, though, there's a pretty wide range of quality from "regular" anodizing. To me, some is even nearly mistakable for HA-III, and maybe that's the case for your light. But I don't think anything beats true HA-III.
Also, I think "thicker" is not always what you want. If it is thick, it could more easily chip. Anodizing is supposed to be something very integral to the aluminum, really changing the characteristic of the metal, and not so much a coating.
My guess is that they are not separate processes, but just different voltages. HA-III uses a higher voltage?? This is something I'm curious about too, and do not know! Maybe someone very knowledgable can tell us. /ubbthreads/images/graemlins/smile.gif