The difference is that they made the mistake, so they have to rectify it asap (assuming there are funds to do so). It was most likily where another customer had put down their correct account number and the bank clerk keyed in the wrong number by accident. So they put it in & take it out straight away & send you a letter just to let you know that the error happened - you're not out of pocket in any way, from what you indicate.
In your case, you made the mistake, therefore the correct account holder must notify them that the funds were lodged in error (I can't see a phone call being sufficent for this)