What exactly is a free stopover. My fare rules say I can have a free stopover in SFO on the way home, but if I do a flight change to stop in SFO, it certainly isn't free

I've booked this
Segment 1 CHC-LAX
Segment 2 PSP-SFO-AKL-CHC

This was a very different price (at booking time), for the same flights on the same day.
Segment 1 CHC-LAX
Segment 2 PSP-SFO
Segment 3 SFO-AKL-CHC

Also if I attempt to make the change now, its also a very different price (again, even for the same flights on the same days)

My fare rules say
GENERAL RULES TEXT
4 STOPOVERS PERMITTED ON THE PRICING UNIT
LIMITED TO 2 FREE AND 2 AT NZD 100.00 EACH.
2 FREE IN SYD/MEL/AKL/LAX/SFO/HOU
2 AT NZD 100.00 EACH.
CHILD/INFANT DISCOUNTS APPLY.