I think the tasman flights operated by short haul are now just the Queenstown service and the occassional substitute for Jetconnect services. The A330 SYD-AKL-LAX-JFK is Long Haul.
Short Haul crew fly the 737 to Noumea (turn around) and from time to time can have Asian trips if Long Haul can't fill them - I know Jakarta went Short Haul for a while earlier in the year.