A student visa (or a limited visa granted for the purpose of study) is required for all people coming to New Zealand to study for more than three months. Study must be the main purpose of your visit.
To get a student visa you have to show you have enough money to meet your living costs during your stay. Make sure you know how much money you’ll need while you’re here studying by researching our cost of living page, and exploring your visa options.
A working holiday visa may allow you to travel, work and/or study for a limited period depending on your age and nationality.
If your main reason for coming to New Zealand is to work then you need the appropriate work visa.
You should also check out our useful information on how to prepare for your move to New Zealand and how to settle into student life here.
source: https://nzstudywork.immigration.govt.nz/work-rules-for-students/student-visa-rules/