Interestingly, in the US the term "spanking" applies to both of the activities you describe. If this is an SEO related questions, take care to slant your SEO towards children, or you could be bringing in a seriously uninterested visitor demographic.
In our vernacular, smacking refers to using the palm for as blow, instead of a fist. So you would smack someone when you are spanking them, and you would smack someone across the face for insulting you, you would smack your palm in your face for a face-palm, you would smack someone upside the head to knock some sense into him.
Here "spanking" is generally used for using the palm of the hand across the someones bottom, regardless of the reason for it. (With the exception of being used to describe an act of self flagellation).
The term "getting your ass spanked" is used to describe an embarrassing defeat.