That's right, and there was a brief controversy here when the Director General and the Prime Minister said that NZ had eliminated COVID and that was taken by most people to mean that it no longer existed here. They later had to backtrack somewhat and explain the difference.

Basically elimination means that the disease is totally under control, and any new cases can be dealt with via testing and tracing. Eradication means that the disease is completely wiped out and no longer exists here.