A stopover is always a connecting flight, but a connecting flight is not always a stopover.

It's a stopover if you stay at the transfer point for more than 24 hours. (The exception being that you can stay for more than 24 hours and not count as a stopover, as long as you're taking the next available flight to your destination.)*

For your example, yes you can use the NZ award to fly SYD-AKL-Pacfic Island - as long as you don't stay in Auckland for more than a day.

* To explain the exception in parentheses above: NZ flies AKL-PPT on Tuesdays, Fridays and Sundays. If you flew from SYD-AKL on a Wednesday, and were booked on the next connecting flight to PPT (on Friday), it would not be a stopover, even though you would be in AKL for 2 days, because you are on the next flight. Convincing a reservation system/person to book it may be an issue though.

In any case if you don't want to stopover in AKL, that's a moot point - you can certainly transfer there in both directions on your 30,000 mile award.

Conrad