A bill is what you owe, not what they owe you
An invoice asks the client to pay. A bill records what you owe a supplier. Reports keeps them apart.
Do not send a bill as the commercial invoice
The commercial invoice is the page the overseas client pays. A bill is your copy of a supplier's charge: freight, parts, a contractor. It stays in your ledger.
Same books, other column
Bills have their own list. Reports has a Bills tab for what is paid, still open, and overdue. They do not count toward the monthly invoice cap.