For coming to New Zealand on any holiday, business meet or for tourism you’ll need a Visitor’s visa depending on the duration of stay. A normal visitor visa i.e. tourist visa allows you to stay in New Zealand for 3 months. If you feel like staying longer in New Zealand rather than your visa allows, you can certainly apply for an extension.
These are known as tourist or short stay visa if you want to visit the UK you can apply standard visitor visa for any of these reasons:
For studying in any of the above mentioned countries that are New Zealand, Canada, USA and UK students need a study permit. A study permit is not any visa. It doesn’t give the candidate any right to board flight to any of these countries.