Are you talking about an address on an existing order, in the order-details screen?
Or about the address shown on the customer's customer-details screen?
There's no built-in facility for changing the details of an existing order, including the address details.
And the address details inside an existing order are completely independent of any addresses in the customer's customer-details screen.
On the customer-details screen, that's neither the "shipping" nor "billing" address. It's the customer's primary address, as in the one the customer has selected to be their primary address out of all their own address-book records.
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