What's the difference between discipline and abuse of my 3 month old child?

At 3 months you can't discipline a child. They have no concept of language yet, much less right and wrong!

I agree with PaulCyp. Discipline or abuse should never be applied to any three month year old. They would never understand either. They will only damage the child's future and their love for you. Children probably don't need discipline until at least when they can walk. And even then it should be mild. Only when they are older can they be disciplined and by no physical means should it be done.

Discipline is intended to help a child. Abuse is intended to hurt a child. And a 3 month old doesn't require either one.

A 3 month old is not old enough to really understand right from wrong. Spanking them is definitely not on at that age, for example.

Discipline is a method to guide behavior. Learning how to study properly is a discipline. Children need to have limits set, but those limits can be set by frowns, finger wagging, raising the voice, etc. Abuse is unnecessary, cruel, and counter productive.