Differences between anger and rage
The American Psychological Association appears to view this emotion as a continuum of intensity, whith annoyance at the mild and rage at the extreme end.

http://www.apa.org/topics/anger/control.aspx

Excessive anger and rage might be caused by suppressing milder forms of anger until this repression becomes unbearable and "the pot cooks over". Psychology Today calls anger a "corrosive emotion": it eats away at you, if you don't express it.

http://www.psychologytoday.com/basics/anger

The continuum and boiling-over idea of anger are nicely summed up in this paragraph of another Psychology Today article:


  Irritation, frustration, anger, rage: these are all forms of anger. And they are feelings first. But when a person’s rage becomes behavior even before thought has a chance to plug in, it is usually because of one of two reasons:  1) it’s been repressed for a long time, and when someone drops the proverbial straw, it explodes; 2) it works for manipulative purposes.


http://www.psychologytoday.com/blog/traversing-the-inner-terrain/201205/is-rage-choice