Anger is the inordinate desire to hurt someone, to seek revenge, to vandalize property, or to ruin a reputation.
Anger or wrath is different from righteous indignation, which is the moral outrage at a gross injustice, such as genocide, racism, exploitation, child abuse, abortion, or terrorism.
Often we hear of people committing a crime in the heat of anger. You and I have no control over what makes us angry, but we do control our response to it. Rage is a form of anger where irrational thoughts of violence overcome a person. Anger as a deadly sin must be deliberate and intentional.
The momentary desire to punch someone who has just waved one finger at me is not the capital sin of anger. Once my reason kicks in, I need to chill out and cool off and look at the situation objectively and dispassionately. (Road rage is an example where anger left unchecked leads to violence.) Making a decision while one is still angry is ill-advised.
Jesus did not show anger but demonstrated righteous indignation when he threw the moneychangers out of the Temple (Matthew 21:12). He did not commit any violence, but He did use what some might call tough love.