When creating an order, the Invoicing email address will be written as the BillTo email on the order. If the Invoicing email address is blank, then the standard Contact email address will be used (on the first screen of the customer). Of course the email address could later be edited on the order to something different.

When emailing, BillTo refers to what is on the document (as does ShipTo), and Customer refers to what is in the customer Invoicing email (unless blank and then it is the Contact email).

Clear as mud?