There are two general sorts of rage - normal (affective) and abnormal (psychotic/schizoaffective) rage.
One may be angry at people without hating them. One for instance may simply wish someone would change their minds about some policy stance without wishing them harm.
Hate is by definition the desire to see loss, injury or even death/destruction come to another.
Feeling homicidal rage toward someone who say, tries to rob, maim or kill you or loved ones is normal. Feeling homicidal rage toward someone because you have worked yourself up into a detachment from reality which places them on the same level of infamy as say a mass murderer, is abnormal.