NZ has quite a lot of octopus species (over 40) but most are not found in the shallow coastal waters, and most of those that are coastal are small.
The most common of the larger species is Pinnoctopus cordiformis (syn Macroctopus maorum - the names are used variably between authorities). But around Auckland you also get the Gloomy Octopus Octopus tetricus which is mainly an Australian species (the NZ population used to be called O. gibbsi). I don't really know how to tell them apart though. Perhaps the aquarists here don't either, or maybe it is just that having a non-specific sign means it can be used for whichever octopus they happen to catch (they have short lifespans of only a few years).