Bill vs Invoice ?

[Geert Janssens]

As a non-native English speaker, I am wondering about the difference between 
the terms "Bill" and "Invoice".

Gnucash uses a "Bill" to indicate a document provided by a vendor and 
"Invoice" for a document provided by a customer.

But in my native language (Dutch, being from Belgium) the literal translations 
of these words have a subtle difference in meaning. Only the Dutch word for 
"Invoice" (being "Factuur") is used in a business context. So we have Customer 
Invoices and Vendor Invoices if we want to differentiate between these two.

The Dutch word for "Bill" ("Rekening") is mostly used more informally, or 
outside of business contexts. I would ask for the bill in a restaurant for 
example.

So how is this in English ? And is it different or the same in the various 
English speaking countries (UK, USA, Canada, Australia,...) ?

Feedback is appreciated, it may help me improve the wording in the Gnucash 
business functions.

Geert