Apples and oranges.

Weather waivers are not cancellations, they are waivers.

If the flight is cancelled you are, of course, entitled to a refund to your original form of payment.

Weather waivers simply allow whatever the waiver says. They generally, but not always, mean that you can rebook without penalty, e.g., if your fare isn't available for a new booking, you may still change to the flight without cost.