To me the distinction between rage and outrage is wrong and right i.e.:
rage = wrong, dysphemism, illogical
outrage = right, euphemism, logical
In common parlance rage is typically ascribed to people who hold some flawed view and are acting agressively towards something while outrage is ascribed to people who are correctly enraged by a situation through their correct view.
So, I would agree that they are exactly the same thing but they are used rhetorically to lead the reader to a conclusion about the person or people who are expressing the emotion even if it is the author of the text.
rage = wrong, dysphemism, illogical
outrage = right, euphemism, logical
In common parlance rage is typically ascribed to people who hold some flawed view and are acting agressively towards something while outrage is ascribed to people who are correctly enraged by a situation through their correct view.
So, I would agree that they are exactly the same thing but they are used rhetorically to lead the reader to a conclusion about the person or people who are expressing the emotion even if it is the author of the text.