How many police forces cover an area then? How is the responsibilty handed out for who does what if you have these different departments? Sorry just very nosy when it comes to others policing. It's interesting.
In the US, you generally have state, county (or parish) and municipal (town, village, or city) police. You also have federal, but they are generally not 'sworn' in the state they work in, and do not perform the typical police duties.
Typically, if a city (town, village, etc) is large enough to have their own police force, they have primary jurisdiction within their own borders for all things not interstate highway-related. However, many (most?) states have state-wide certification of all peace officers, so they can make arrests anywhere in the state if need be, can carry their weapons concealed off-duty, etc. However, unless they are in 'hot pursuit', their normal jurisdiction ends at the city limits. They are generally known as police officers.
A county will have a sheriff's office. They're responsible for primary law enforcement for all areas inside the county but outside the city limits of the cities within the county. Typically spread much more thinly. They also provide backup for city officers when necessary. Often, the county will also provide the detention facilities for all agencies except federal inside the county, so the 'jail' is a county lockup with county detention officers running it. Officers are typically known as 'deputies' rather than 'officer'.
States have either state police or state highway patrols. They are responsible for primary law enforcement of state owned lands and highways. They are quite often doing more in the way of DUI, speeding, drug interdiction, and so on than they are taking reports on burglaries. However, states also generally maintain crime labs and have their own investigative divisions, and they'll often be asked to get involved or to actually take over and direct investigations involving multiple jurisdictions or cases that are just too big for local county or police to handle. They are often known as 'officers' but can also be known as 'troopers'.
This is just general, not hard-and-fast rules. But in general, the state troopers write speeding tickets on the highways, the county transports drunks to the county lockup, and the city cop writes you a ticket for running a red light in town.
All of them are usually sworn peace officers, whose arrest authority covers the entire state.
Primary jurisdiction for interstate crimes goes to the FBI. Their officers are known as 'agents'. There are many, many, uniformed and plain-clothes law enforcement and investigative agencies in the federal government, from US Marshalls to Border Patrol to Forest Service Police to Railroad Police but most do not or cannot perform local policing or make arrests for non-federal crimes. An FBI agent cannot write a ticket for speeding, for example.
Oh, and by the way, something I found interesting from long ago...
The most 'powerful' police officer in the USA? Railroad cop. They have federal, state, and local jurisdiction over any bloody thing they want. Tradition dating back to the days of the Pinkerton Detective Agency. Most people don't ever see a railroad cop, but they've got amazing arrest and jurisdictional powers if they choose to use them.