It's a good distinction, so I asked what would happen in each of the three cases. I think that's one of the trickiest parts of this concept.
In a country as armed and violent as the United States, escalation happens quickly and dangerously. We've all seen videos of officers pulling a car over for speeding and being executed the moment they look away, there's been more than a few in the past couple months alone [1] [2] [3]. Nearly any situation can become lethal for the officer and civilians [4], so I think it's fair to ask in what situations there would be an armed responder.