There are three general approaches, which are commonly used to move the funds between different places (such as bank accounts).
Bank wires (often referred to as bank transfers) do not take long to clear and are, perhaps, the simplest and the most common way to move your money from one place to another. The approach is not quite what you need if you need to clear large batches of transfers at a time, and every single bank wire does involve a cost. SWIFT is a common and universal payment system, used for bank wires worldwide.
Bank drafts (which are sometimes also called bank transfers) are accomplished through clearing houses. In the US the system for bank drafts is the Automated Clearing House or ACH. Respective clearing houses in the UK and the EU are BACS and SEPA. Bank drafts cost less than bank wires, and they can be processed in large batches. However, they take more time to clear.
Transfer of funds through debit networks. If you are in the US, in order to save on interchange cost, you might want to limit your choice to PIN-less debit networks, regulated by Durbin amendment.
You can find more information on bank transfers in the respective article on #Paylosophy.