ACME requires a minimum of First Name, Last Name, and one of Phone, Email, or Address (Zip if at POS) to create a customer. When the minimum required data to create a customer is entered during checkout, those orders will have the appropriate customer fields and billing fields filled, in addition to having a customer ID associated to the order.
Most commonly, orders will have the same information in both those sets of fields. In the case of a member order, the primary cardholder will automatically be the customer on the order, and the billing information will only differ if, for example, a credit card with a different name is used on the order.
Billing data is just saved to the order and will not have a different ID associated, like a Customer or Contact would.
The difference for organizations is that the order contact is going to be in the contact fields and billing will be whatever is entered at the time payment(s) are made. If the order is initially created without any payment taken, there will be no customer. If the order is created with any payment, the customer will be the same as the first billing data entered at that time.