We can look at it more closely. Anger WITHOUT CAUSE is what murder is. If you are extremely rude to me and I am angry, would that be anger with cause or anger without cause?
But I tell you that anyone who is angry with his brother will be subject to judgment. Again, anyone who says to his brother, 'Raca, 'is answerable to the Sanhedrin. But anyone who says, 'You fool!' will be in danger of the fire of hell.
Matt 5:22
Anger is for war, aggression, violence.
Annoyance is about irritation and identifying a problem.
The phrase "his brother", restricts murder with anger to those in ones family of believers, not an
enemy, or unbeliever.
We have no reason to be angry with a fellow believer, but what about a blasphemer,
or apostate?
On the subject of anger, the verse you quote maybe wrong.
The problem with the phrase "without cause" is not in all the copies of the gospel,
and seems a cop out. One could dream up lots of causes in ones own mind.
Now murder is a single act, angry is an emotional feeling that goes on.
Paul puts it like this
"In your anger do not sin": Do not let the sun go down while you are still angry,
and do not give the devil a foothold.
Ephesians 4:26-27
Paul seems to be saying anger will happen, but resolve it, or it becomes equivalent
to murder.
Now this thread is on salvation and not anger, being saved by faith and not works or
being a good person.