Do I take the same rental car on the ferry between the islands?

This depends on the rental company and the arrangements included in your package. Some vehicles can travel aboard the Cook Strait ferry, allowing you to continue with the same car.

Other packages require you to return the North Island vehicle in Wellington, travel across the strait as a passenger and collect another rental car in Picton. When separate vehicles are required, both car bookings and the ferry crossing are coordinated as part of your Both Islands itinerary.