For the most part, police presence varies from state to state in the US, so this may not be 100% (I'm not from Florida, but it's not that big of a variation, I'm sure).
Most cities have their own police force. Those officers handle any law enforcement matters within their district.
Then some counties, or even sometimes groups of cities, have a regional police organization that covers the area agreed upon. In the case of a county, they would be able to do any police duties within the county, but generally would not cover a city with its own force. The regional police would usually be a sheriff's office.
State Troopers (in some states, State Highway Patrol) are generally responsible for state highways, but can also respond to other incidents, especially in rural areas that aren't served by a local or county police force.
Also, resources are shared in cases where the local departments don't have the capacity to handle certain crimes (for instance, a small town doesn't have a crime lab, so they turn a murder case over to a major crimes squad from the sheriff's department).
Each department can have its own ranking system of officers, from patrolman up to Chief.
It can get a little confusing, but I hope that helped a little.