"Shipping address is same as billing address" or the other way around?

Some online shops follow these guidelines (case A):

  • Let user enter a billing address.
  • Have a checkbox "Shipping address same as billing".

Some other online shops do it just the other way (case B):

  • Let user enter a shipping address.
  • Have a checkbox "Billing address same as shipping".

In case A, it seems that the primary view of the checkout workflow is to generate an invoice, whereas in case B the checkout process is seen as a step in the workflow to finally ship the actually product being ordered to the customer.

An example for case A is WooCommerce, an example for case B is Shopify. Amazon also seems to prefer case B.

My question:

Is there any real reason to prefer case A or case B?

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