The legal standard is supposed to be the same, except cops absolutely have the right to use deadly force against a fleeing felon. The reason civilians are held to a higher standard than the police is that the police and their enablers in the legal system are easy on each other, and they act to advance their "monopoly." Lots of ways the dual standard can be implemented.
Cops are legal "insiders," are the system doesn't police itself well. See too, judges and prosecutors. All on the same team, one hand washes the other.
That is not true anymore and hasn't been for decades.