Is this sign the same as the sign for 'slap'?
They are very similar, but context matters. This specific sign represents the disciplinary action of spanking. If you are talking about slapping someone's face, you would typically mimic slapping your own cheek instead.
Do I need to make a loud clapping sound when I sign this?
No, you do not need to make a loud sound. While a slight clapping noise might naturally occur when your hands meet, American Sign Language relies on the visual movement, not the sound.
Can I use this sign to mean 'punish' in general?
It is best to use this sign specifically for the physical act of spanking. There is a distinct, separate sign for 'punish' that involves striking the index finger of the non-dominant hand.