With separate tickets, you leave Auckland airport to collect your bags: it's the entry rules of the country (New Zealand) that count. With a single ticket you often stay airside: the rules can differ, so check them with the airline.
1
No visa
For a short stay, your passport is enough.
60
Online formality
Electronic authorisation or e-visa, often paid, to sort out before you go.
137
Visa required
A visa to get in advance: avoid these stopovers with separate tickets.
Rules as of 12 January 2025, source: Passport Index. They change: check with the embassy before you go.