It looks like they are related to Paymark, because I have noticed some references from the paystation.co.nz website to Paymark:
I have got a response from Paystation:
Paymark is the national switch in New Zealand.
We have our own API.
Unless a gateway like Paystation has a direct integration with a bank, then they need to integrate with a switch like Paymark (there are others, but these are international providers) to process the transaction request between the card holder, and the merchant.
Paystation have been integrated with Paymark in various forms since 2002.