This is highly local, I would assume. Here is one US option.

1) Bill Pay = Automated payment services that can be set up at financial institutions. The customer provides the bank and company with debit information and bills are withdrawn automatically out of a checking account and reported in monthly statements.

Read more: http://www.businessdictionary.com/definition/bill-pay.html#i...

2) Automatic Bill Payment

Routine, automated payments made from a banking, brokerage or mutual fund account to vendors. The automated function can be initiated either with the source of funds (the bank with the checking account) or the vendor to whom payment is owed. Automatic bill payments occur over an electronic payment system, such as the Automated Clearing House (ACH).

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Note added at 5 hrs (2014-03-22 00:24:07 GMT)
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The European-American difference:
http://en.wikipedia.org/wiki/Standing_order_(banking)



Standing orders are available in the banking systems of a number of countries, including Germany, the United Kingdom, Barbados, the Republic of Ireland, India, Netherlands, Russia, Pakistan and presumably many others. In the United States, and other countries where cheques are more popular than bank transfers, a similar service is available, in which the bank automatically mails a cheque to the specified payee.