Police ARE treated differently; the average person who uses lethal self-defense runs a very high risk of prosecution, or at least that’s the impression I have. Police, on the other hand, are presumed - rightly or wrongly - to have more of a right to use force than the average person, and so when they do use lethal force, it is thoroughly investigated before any charges are filed.
White police who kill blacks are treated much differently too... it is generally assumed they acted with racist motives, even with no evidence. Of course, the GOP jumps on the bandwagon too, to appease the mobs.