What is the difference between this two sentences?
A: Go to New Zealand on business.
B: Go to New Zealand for business.
Is there any difference in how these would be interpreted?
There isn't much of a difference here. In sentence B you're using the sentence structure
{Do something} for {Reason}. Examples include:
Sentence A uses a specific kind of English idiomatic phrase {Go somewhere} on {type of time}. By 'type of time' I usually mean something like "business" or "vacation". Examples include:
but not
If you're ever unsure whether to use "on" or "for" in that type of sentence, "for" almost always works, and "on" is only correct for a specific few cases. For example, you could say "Go to New Zealand for February" and that would mean you were spending the entire month in New Zealand.