Now, it's true that there are further meaningful intent-based distinctions you can make within the broad category of abuse, but that's somewhat beside the point.
That doesn't sound correct to me. If a little get (well below the age of reason) reaches for the pretty red glowing burner atop the stove, you slap away his hand because the small pain of getting his hand slapped will serve to make a second attempt less likely, and the small pain is far less severe and more transient than the great and lasting pain of a nasty burn.
Enjoying inflicting pain is definitely abuse, but inflicting it to prevent worse pain and suffering is IMHO not.
[0] https://www.mercurynews.com/2017/12/29/new-york-city-mayor-1...
No, you don't; if they are well below the age of reason, they are well below the age at which they will connect the hit with the reason for it.
That's why you don't let kids that young around a stove in the first place, and if they do get loose around one, you restrain and remove them. This may involve incidental pain, but not intentional, instrumental pain.
Not trying to detract from your overall point, just thought it was worth noting.
What? This is just child abuse. Please expand on what circumstances in which this considered OK?