what is the difference between police, sheriff and State Troopers?

Question

I’m fairly new to living in the US and I see all three on the roads here. In the U.K. we only had police.

In: 24

Answer 1

Police are just public sector employees.

Sherrifs are elected.

I know State Troopers have jurisdiction over entire states but I have no idea where they come from, who chooses them, and why their hats are somehow both ridiculous and intimidating.