"Type II" or "ii" can imply different things, with the common denominator simply being something allegedly improved over its previous version
Some major change must have occurred some 15 years ago or so. The Crystal Archive before that time was qualitatively superior (longer shelf life without fogging, higher dmax, no mottling, heavier base) to the Crystal Archive produced today. I've used them side by side and the difference is massive. The 'old' CA was more like DPII or Maxima today (according to an Fuji engineer I talked to about this and my own experience confirms). I still have a tiny bit of it and it wouldn't surprise me if it still printed fairly well today despite its advanced age. Don't try that with present day Maxima, which will visibly shift colors and start to take on lime whites after a year or two.
And how "DPii" dovetails into all this is darn hard to figure out on this side of the Pond - the mere listing of it has come and gone; so is it the same thing as "CN" or not ???
I think I've confirmed this to you after having asked Fuji about it roughly a year ago. You'd have to look it up; it's on the forum somewhere. Things changed in particular when the US plant shut down in Sep. '22 (IIRC); after that, one or two of the product names appear to have been continued while the actual product and its source changed.
Maxima seems to be a rumored ghost nobody has actually seen.
It doesn't sell as well as Fuji would have liked, apparently. Its production volumes are likely a shadow of the mainstream papers, so it's not always available in all desired sizes and finishes. However, on this continent, it's fairly commonly available. The problem is that virtually nobody is willing to pay the premium for Maxima especially because its performance in digital exposure is virtually indistinguishable from DPII - which does sell, and is also available in smaller rolls. Ironically, for us darkroom printers the Maxima / DPII difference is more relevant than for its intended market, and of course part of the benefit of Maxima is in the longer lifetime of the processed prints, which is apparently something only a tiny fraction of the market is willing to pay for anyway. I guess that's a big part of the story why you virtually can't get hold of it in the US. I think the US branch just doesn't bother ordering it since it'll just sit in a warehouse until they have to recycle it.
And the FujiflmUSA website doesn't untangle the question in a satisfactory manner.
Fuji hasn't succeeded yet (and possibly never will) in streamlining information provision, mostly due to the high degree of autonomy that the branches enjoy. It's common for the people at manufacturing to hear about information that's outdated on e.g. the US website and there's basically not a darn thing they can do about it. For products like Super Type CN and the 'portrait' paper you mention it's virtually impossible for an outsider to figure out which products these actually are. And probably for most Fuji personnel, too.
The TL;DR is and will always remain: buy what's available, evaluate it and if you like it, buy some more. We may have a decade of fun left in this niche, so let's ride the wave as long as it lasts.
