It would be illegal in both NZ and Australia to lump them together. In NZ the minimum is 5 days per year sick leave (even if you only work 1 day per week) while in Australia it is 10 days but that is for a person working 5 days per week, so a person working 1 day per week only gets 2 days sick leave (now called sick and carers leave so you can take time off for a sick child).
As a teacher, my vacation days were of course fixed (about 55 days) but I had 22 days sick/carers pay on full pay and another 22 days on half pay per year. I think 20 days accrued to the next year and, as I never took more than 5 days in any one year, I had a huge amount when I left but I did not get pay for them.
I only took it as carer's leave once when my mother (aged in late 80's by then) moved home. Some women teachers seem to have a sick child every 2 weeks and knew in advance (as they booked all their classes for the day into the library which annoyed me as the teacher/librarian).
I did occasionally have a "sick of work" day but never more than 2 or 3 in any one year and, as said, never more than 5 sick days in any one year.