It goes by jurisdiction size.
Police are at the municipality level (towns and cities) and will typically handle anything that stays within their municipality.
The Sheriff’s department is at the county level. The head of the department, the Sheriff, is elected. The officers working for the department are Sheriff’s deputies. They handle anything covering multiple towns in their county, and act as the primary law enforcement for any town too small to have its own police force.
State troopers cover the entire state. Normally you’ll only see them on freeways, as people on them can quickly move between counties, and local law enforcement can typically handle everything else.
Then of course there’s one more level, federal. The FBI deals with federal crimes and crimes committed across multiple states.
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