The difference is that a hate crime has no justification. If a wife kills a husband, or vice versa, they may or may not have a good reason, but at least they think they have some justification. When there is no motive other than just hate for some unknown person because he belongs to some group, that is of a greater danger to society.
Of course, if you give out a 30 year sentence with no possibility of parole, it is going to have the same deterrent effect no matter what the motive is.
All murders are committed by people who are not quite sane. A hate crime is committed by someone a bit more of a psychopath than someone who is motivated by jealousy, greed or some other motive based on what they think the victim did to them.