To clarify terms - in New Zealand Wild camping is not a widely used term. If you are to use it here, people will interpret it as back country camping (well away from roads). Freedom camping is used as a term for camping outside of designated camp sites. If by wild camping, you mean road accessible, unserviced camp site in a remote location, New Zealanders refer to this simply as camping.
The freedom camping act does not distinguish between vehicle supported, RV and Tent based camping. There is a recognised standard for Self Containment for RV's - commonly referred to as Certified Self Containment (CSC). Camping close to roads is now widely restricted to RV's with CSC - in effect freedom camping is severely restricted unless you have an RV with CSC. In some areas freedom camping is practically banned as its limited to a very few location. Most Local Authorities have $200 fines for breaking the rules, and its commonly enforced (often in the early hours of the morning before sunrise).
If you want to camp in remote, unserviced camp sites, DOC has a large number, typically $6 /per person per night - often with very limited facilities. There are a lot of other places where its allowed and a number of low cost camp-sites offering basic facilities and safe, legal camping.
A good web site for detailed information of places to stay and the rules around them, visit Rankers.co.nz
Where you are well away from roads, on a vast majority of DOC administered land camping is acceptable.