This is a very simple explanation for kids to learn the difference between feeling an emotion we all feel, vs. affecting others in a negative way when angry. After introducing this concept, I have used it many times to explain the difference in behaviors, the main difference of course being whether other people are hurt by words or actions. The first concept to teach (and not obvious to all children), is to teach them that feeling angry is normal and ok. To many of them, they see this as throwing a tantrum is ok, so teach them the difference! Then teach them ways it is ok to be mad (insert coping skills and outlets for anger here) there are a few examples on this list, but basically following through with what you have been teaching them, and using the alternatives to hurting others.
This concept is also useful as a way to work through ways they have reacted to situations, helping them understand the difference using real examples. This is also a simple and easy prompt to help when they are angry, reminding them it is ok to be mad, but not ok to be mean, then give them some "mad" choices.