The distinction that you are trying to draw is the distinction between motive, which is not typically an element of the proving a criminal act
Is that really true? If you kill someone for money isn't the penalty greater than if you kill them out of anger?
The answer is, it depends, of course
If you killed them out of anger and there was no malice aforethought, therefore rendering it 2nd Degree murder (in many states), then that would be a lesser crime than premeditated murder (murder for hire which I think is what you are talking about). But, that's not really motive that makes the distinction. It is a recognition in the law that people do, in fact, get angry or have fights and the consequences are greater then the participants intend or suspect. In some cases they are not reckless but are intentional, but not premeditated.
If I'm armed and get in a fight and at some point pull out my pistol and shoot the guy, that would be second degree. If I get in a fight and then go back to my house and get the a gun return and kill the other party, that's premeditated murder. The penalty is higher for obvious reasons.
lol.. of course it depends.
what if you were seething... hated this person so much that the very thought of them drove you to a red-hot rage? you go out and happen to find the person and without the slightest provocation, or minimal provocation (like the person smiling at you), you lash out and kill them. would that be pre-meditated? after all, you didn't go out planning to kill them... or would it be temporary insanity? no... b/c you knew you were killing the guy and hated him... so? what is it? this is probably the closest situation to a hate crime... the rage against a group become so great that either with little planning or momentary response, you attack the person or group of people.
Now... society can't send a message that say, Tech Esq can't hate rude people so much that the sight of one sends him into a blind tizzy... but society CAN send a message that society won't tolerate people being killed for what they are born.
as to your last point, if you were lawfully armed and were lawfully defending yourself with reasonable force, you wouldn't be guilty of anything, not even second degree.
only if the use of force were excessive would that come into play, I think.