Do I need seperate harnesses for a buggy and wagon?

I have had driving horses in the past, and now I'm starting to train my 13 year old Arab/QH to drive also. All of the training articles I have read are for training a horse to pull a "cart" or buggy, but I own a full-sized wagon/carriage. I have a used nylon horse-sized harness that was used on a "buggy" horse, but will that same harness work on my wagon/carriage?