The Consuming Power
For a while now I've been wanting to analyze the difference and main aspects of both Rage and Hatred. First we begin by the dictionary definitions.

Rage:
1. a : violent and uncontrolled anger b : a fit of violent wrath c archaic : insanity
Hate:

1 a : intense hostility and aversion usually deriving from fear, anger, or sense of injury.

Even though they seem to refer to almost the same emotion, even by looking at the definition we can see the nature of both is different.

Rage, often associated with fire, is as said, uncontrolled. Rage comes as a severe reaction to an event. Rage usually bypasses all rational judgment, fueling one's desire to action. It makes them act violently, being straightforward and trying to solve the problem instantly. The downside, is that when ignoring all rational thoughts, one is very prone to make some mistake, or take an action they might regret. It can be seen as something that consumes the body, empowering it, while rendering one's mind disabled. It make your body more ready to take action, ignoring fear or personal safety. Any animal trying to protect their young from predators, is showing anger.
Hatred works very differently. Hatred is not something one suddenly feels, it does not lead to immediate action and it does not cloud someone's judgment. Hatred is a byproduct of other emotions, if one can't properly process one's emotions, they might end up turning into hate. Being mistreated, abused or psychologically wounded may lead to hatred. Hatred has a point, it's own agenda, and it leaves one's mind free to calculate, think and plan how to complete this agenda, with least personal damage. Hate does not prepare the body to do anything, it occupies the mind to think, but the mind is left intact, but there is one problem with hate. Hate consumes the soul. It changes people's attitudes, the way they see the world. It kills innocence. It may not lead to action, but those willing to take action, are likely to do something drastic.
None of these are good to feel. While anger may lead to a solution to an immediate problem, it does not last, it leaves no scars, but the occasional regret of some action taken. Hatred on the other hand may seem like a way to end pain and other negative emotions, but is a one way road, it consumes and changes.