Is it a hate crime if you attack someone because you hate that they're rich? Is it a hate crime if you attack someone because you hate blue shirts and he was w

Is it a hate crime if you attack someone because you hate that they're rich? Is it a hate crime if you attack someone because you hate blue shirts and he was wearing a blue shirt that day? What exactly is a hate crime and how is it precisely defined such that it's more serious than crime in general? If you punch someone in the face vs Punch them because they are a woman vs Punch them because they are white vs Punch them because they are black vs Punch them because they are gay vs Punch them because they are a nazi vs Punch them because they are a commie Which of these is a hate crime and which is a "normal" crime. Which get punished more harshly and how to decide the motivation other than in the absolutely most obvious cases of the person confessing why they did it.