This is very interesting. According to stats provided here [0], 77.5% of New Zealand's population are "fully vaccinated" against COVID. I think differences probably due to selected reference population, your figure is percent of eligible (>=12yo) whereas the number I found is per whole population (including those < 12yo).
In any case 77.5% is pretty impressive, by comparison the US fully vax percent is lower at 65.2%/total population. Also NZ confirmed cases == 7.0% of population, US == 24.2%. Big difference there.
Not sure what set of factors accounts for diff in cases rate. NZ may well have done more to keep the virus from spreading. On the whole though many more questions about COVID than answers.
I'd also guess data collection and reporting practices vary a lot by region or country. Makes data hard to compare and in turn makes it hard to assess what works and what doesn't. I'm keeping a good thought better solutions will emerge.
[0] https://github.com/CSSEGISandData/COVID-19