A bill is a request for goods or services which were received. It contains a list of services or items and the due date. Issuing bills is a common practice in restaurants, credit card companies, utilities and other service providers.
Bills and invoices are often used interchangeably and there is no difference in the results they produce. Invoices are commercial documents which contain more information (e.g. seller's and buyer's address, method of payment) than bills.
The use of these documents is determined by circumstances.