If you are in a rage, your temper is out of control or violent. If you are outraged, your temper is NOT out of control or violent, but you are extremely upset or disturbed by something.

As nouns the difference between them is that rage is violent uncontrolled anger, fury, violence of feeling, desire or appetite, enthusiasm, fervor and even insanity, while outrage is excessively violent or vicious attack, wanton cruelty, anything that strongly offends or a powerful resentment or anger aroused by something perceived as an injury or insult. As verbs the difference between them is that rage is to act or speak in heightened anger while outrage is to cause or commit an outrage upon; to treat with violence or abuse.