I've been a parent. I believe in spanking a child with your hand as a necessary tool of child discipline. But it's not the only tool. You shouldn't strike a child simply because you're angry or frustrated.
I believe that striking the child with anything else is child abuse. So is leaving marks or bruises on the child. What do you gain when you use a stick to beat them with that you can't accomplish by hitting them three times on the butt with your hand?
You really need to know your child and know what corrects them. I believe in spanking when they're defiant or when they continue to immediately disobey. Sometimes the child isn't happy until they're shown what the limits are.
Some children are very sensitive. Just hearing the anger in your voice crushes them. It serves no purpose to be brutal in their punishment. Making them stand in the corner for a couple of minutes is more than enough for them. Usually girls are the sensitive ones but sometimes boys are too. You need to know your child well enough that you're not using more correction than necessary.
It's also wrong to yell and scream at your child. To call them names. To verbally abuse them. You're the parent. You shouldn't have to yell, scream, or threaten. I tried to keep a calm voice and be police. If you expect the child to be polite you need to be polite to them. You need to teach them that there will be immediate consequences to their slow compliance as well as their misbehavior.
I use a lot of methods in my class to enforce rules and consequences. You are right by pointing out the peculiarity in dealing with different children. Some children will not even be moved if you deprive them of some privileges as a consequence for their action. I have a case of a girl like that in my class. However I noticed she doesn't like it when her name is being mentioned openly in the class as a rule breaker. So anytime I tell her I will mention her name in the class and tell them she broke a rule, she would adjust.