In the pro era... and collectively... correct. Also since readmission we play NZ frequently where in the amateur era it was occasional tours...
SA still has the best record against NZ, of competing nations, although in the last 10 years that is probably Ireland.
Since readmission (1992) which more or less coincides with the pro era (1994) the head to head vs NZ is as follows:
Played 69, NZ have won 47, SA have won 20 and there has been 2 draws....
In the amateur era Played 37, NZ won 15, SA won 20, with 2 draws
In the last 10 years Played 19, NZ won 12, SA won 6, with 1 draw