Pretty bad comparisons. Awful, actually. For different reasons, though. I don't know why people keep making these terrible comparisons.
New Zealand is basically Colorado, in terms of land mass and population. So, you're talking about a whole country that's the size of one US state. The logistics are not at all comparable.
South Korea is even smaller, roughly the size of Indiana. There is a much greater population, but with such small land area, it's again much easier logistically to coordinate a response.
The US is the 4th largest country in the world based on land mass. On top of that, we are comprised of 50 individual states, each with their own state health departments. And within each state, many counties have their own health departments. Each state is free to set their own guidelines, sometimes even on a county-by-county basis. There are over 3,000 counties in the United States.
Countries like New Zealand and South Korea don't have to worry about such layers of complexity. They just say "this is what our country is doing." For their miniscule size, it's FAR easier to marshall resources and implement interventions.