A more specific, but not commonly used, term is "giro transfer" (coming from an Italian word). That's a payment where the sender pushes money, as opposed to the receiver pulling it, as they do with a cheque or a card swipe. In the past you'd send a letter (which is why it was inconvenient), but nowadays you log into my online banking page, enter a destination account number, amount of money to send, and a note, and click "send", and the money is transferred somewhere between immediately and three working days depending on which system you're using. This capability is very obvious to non-Americans and I'm sure even to Americans, is an extremely obvious thing that any banking system should have...

The key difference here is that you communicate with your bank, giving them a direct instruction to send money to the recipient at their bank. With cheque or card, the recipient communicates with the recipient's bank, to forward an authorization written by you, which is sooner or later verified against your bank. Which is convenient for you, but involves more steps.