When buying a 2nd hand car privately,

Thats because Westpac only allows you to schedule a payment (as explained above).

You raise a good point though, if you can't tell the difference between scheduling a payment and an instant transfer with a confirmation screen showing as such then use another method of payment. BTW before someone points it out, an instant payment still won't arrive at the other persons bank any quicker it just can't be cancelled easily by the initiator and shows a debit straight away from your account. That's why many business's accept a screen shot as confirmation of payment. Now what I can't remember is whether Westpac show a credit hold against your account for the amount you schedule. A Westpac person may be able to confirm/deny that.

I do admit it is a potentially confusing point of difference and I clearly haven't explained it well enough given the above comments. Sometimes when you have been immersed in things you forget how new and confusing it can be to others. If I had realised how confusing this is and that Westpac still only allow scheduled payments I wouldn't have suggested using this method, point taken.

Of course if both people bank with the ASB then theres no issue -the money shows up in seconds.

I couldn't do it but the OP could

Some other banks do within themselves as well. Here is what I recall, don't count on this to be accurate as I am remembering back a number of years and things change. My memory is also only so good, so use this information very much at your own risk. or better yet just check with the bank involved first!

Westpac - No
ASB - Yes (as pointed out)
BNZ - Yes
ANZ - Used to be but I suspect they have changed this recently, I know there was word they were going to. May have even changed back to allowing it with text banking.
National Bank - Can't remember for sure but don't think so.
Kiwi Bank - Can't remember
Text banking and smart phones came long after my time so I don't know how that affects things.

Incidentally. there is actually another same day electronic method of transfering money between any bank that people seem to have forgotten about. That is the Telegraphic Transfer system, yes the same one you use for international transfers. I can't vouch for whether all banks allow this but certainly ANZ does or used to, there is no reason the others can't do it if they let you. Its not cheap (was $25 last time I used it) but can be very handy with large transfers sometimes.

It may not be absolutely instant, I can't say I have tested it to the minute.

Transfers from one account owner to another within ASB are instant.
Transfers Kiwibank account to kiwibank account is instant
Transfers BNZ to BNZ are overnight
Transfers National to national are overnight
Transfers Anz to ANZ are overnight
Transfers westpac to westpac are overnight.
Transfers from one bank to another are USUALLY overnight
The exception beggars belief--ANZ to National can take 2 working days.
Payments by POS are in most case limited to $2000 per day
The exceptions are Kiwibank and westpac which can be unlimited.
However
National bank/anz bank is open 7 days a week at main centres -nomal trading hours sat and till 2 on a sunday
Asb Bank is the same.
BNZ in Auckland have 2 branches almost 24 hours -One is in skycity casino the other at the airport.