Do all countries such as New Zealand belong to a continent?

Geographically, a continent is a single continuous land mass. Culturally, island nations are often grouped in with nearby land masses to be considered as part of a continent. The specific case of New Zealand is considered part of the cultural construct of Oceania, a 'continent' whose largest landmass is Australia, and which includes a number of island nations in the Pacific Ocean. There are many island nations that are not considered to be part of any particular continent.

https://en.wikipedia.org/wiki/Continent

https://en.wikipedia.org/wiki/Oceania