Marc Daalder has a good article at Newsroom which discusses the difficulty with the 90% vaccination target given the different statistics for population that are in-use. The central point is that two major government bodies disagree about the total NZ population by about 122,000 people. Clearly, that's a significant difference.
The Ministry of Health uses health services uptake as a measure, or HSU, which is the lower number. Lots more detail is available at this link. This may under count younger people, who may have never accessed health services, especially if they are migrants. If they haven't even used a health services they may be less likely to get vaccinated.It would explain why some segments of the population appear to have vaccination rates greater than 100% (see example below from a Spinoff article).
On the other hand, it may be more accurate for older lives than Statistics NZ, which estimates from the 2018 census using a quarterly adjustment for births, deaths, and migration - a good explanation of how this is done and the resulting numbers is at this link. The article is well worth the read. It also underlines the wider problem of belief in one right number. These things are difficult to get right and there are some good arguments in favour of different methods. We often have this difficulty in our sector where different people and companies have different preferred measures and there is often a surprising difference between the results each measure generates.