Following British (English) practice from the 19th century onwards, in New Zealand it is unusual to separate the constitutent peoples of the United Kingdom and count them separately. They are often collectively lumped as British and often even Irish are added into the pot and treated as the same.
In New Zealand's national consciousness it seems we have four major groups: British/Irish dexcent New Zealand Europeans (Pakeha), Maori, Pacific Islanders, other European descents, other ethnic groups (Chinese, Indians, etc).
The Lowland/Highland split is one between Germanic Anglians (including Anglicized Picts and Britons) and Celtic Gaels, whose remote forbears originated in Ireland, though with considerable Viking and Norman mixture. Despite their cultural and linguistic differences, both Highlanders and Lowlanders were predominantly Calvinist by the time of their migrations to America. Whether Lowlander, Highlander, or Scots-Irish, their concepts of liberty of conscience and the duties of rulers to be subject to law strongly impacted the formation of this republic.