For the payment methods, we have the Manual payment method "Bank Deposit" active.
Since the "Order invoice" description on the 'Notifications' settings pages says: "Sent to the customer when the order has an outstanding balance.", I was expecting the customer to receive the "Order invoice" notification, upon completing their order with this payment method.
However, instead of the "Order invoice" notification, our customers receive the "Order confirmation" notification in their mailbox (which is strange, because they still have an outstanding balance?!).
So, my questions are:
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This is an accepted solution.
Apparently, "Order Invoice" emails are only send in response to a manual action, as described on the Manage Orders help page: https://help.shopify.com/en/manual/orders/manage-orders#email-an-order-invoice-to-a-customer