Three routes, and you can mix them: DelivAZ drivers, your own drivers, or collection from your store. Nothing is forced on your shop.
Mark the order ready and a driver collects it from your counter and takes it to the customer's door. You follow it through every stage from your panel.
The delivery fee is worked out by distance and shown to the customer before they confirm - it is never taken out of the price you set. Where the customer pays on delivery, the driver collects it and it reaches you.
If you already have drivers, keep them. Set your areas and their rates from your panel and deliver as you do today, while the customer still sees where the order is.
Or open collection: the customer orders and pays online, then comes by when it suits you both. You can run all three at once and let the customer choose.
Delivery is a setting in your panel, not a commitment made at sign-up.