There are only two marine crayfish around the coastlines. J. edwardsii is the commonest species in NZ - it's the usual species in aquariums/restaurants/anywhere else. The Packhorse Crayfish S. verreauxi is also common but can be easily distinguished because it has a smooth tail section (prickly/knobbly in edwardsii). It is also considerably larger when full-size.
The only other marine crayfish species in NZ are the deepwater Projasus and the tropical Panuliris (in the Kermadecs, at the extreme south of their range)