Thanks for giving the link to the CAPAD.
> "In Australia there is no general relationship between the title given to a protected area and its IUCN category."
Yes, may be (but on WDPA I find IUCN categories ... and II for "National Park" is ok). But titles doesn't greatly matter. Tagging should be primarily based on the IUCN category because titles can be misleading. First search an IUCN category: the Tagging-scheme is "based" on the IUCN categories from the WDPA. "Generally" the given fits for protect classes.
If there is no IUCN-code, don't focus only to the title, but check primarily with your administration or NGO's the intentions, objects and instruments of protection, if they accord to the protected_area-classification descriptions. The title itself is sometimes misleading - because of politics or cultural characteristics or ignorance.