Sheriff's Office vs Police Department

Is there a difference between Sheriffs and Police?  YES

Black's Law Dictionary defines the terms as follows:

DEPARTMENT: "One of the major divisions of the executive branch of the government....generally, a branch or division of governmental administration."

OFFICE: "A right, and correspondent duty, to exercise public trust as an office. A public charge of employment... the most frequent occasions to use the word arise with reference to a duty and power conferred on an individual by the government, and when this is the connection, public office is a usual and more discriminating expression... in the constitutional sense, the term implies an authority to exercise some portion of the sovereign power either in making, executing, or administering the laws."

The Office of Sheriff is not simply another "department" of county government. The internal operation of an Office of Sheriff is the sole responsibility of the elected Sheriff. County department heads are subordinate to a county governing body, because a "department" is truly only a division of county government.  The Office of Sheriff is a statutory/constitutional office having exclusive powers and authority under state law and/or state constitution.  These inherent powers are not subject to the dictates of a local county governing body.

The Office of Sheriff has inherent common law powers and sovereignty granted under a state's constitution and/or state law.  It is different from a county department which derives its limited authority from whatever is delegated to is by statute or by state constitution.

The use of the term "Department" implies being a subordinate unit of government (i.e.  subordinate to local government - "delegated" authority from county government to a Department). The use of the term "Office" implies inherent powers and independent sovereignty.

From: http://www.sheriffs.org/content/faq

A police department is hired by a city government such as a mayor or city council.  A police chief is not an elected official.  He or she is a city employee.  Police have jurisdiction in their town.  

Sheriffs have jurisdiction in a county.  Deputy Sheriffs are hired by the Sheriff and patrol the entire county.  Where police may patrol only a few square miles (filled with thousands of people), Deputy Sheriffs patrol hundreds of square miles... often by themselves with little or no backup.  

Sheriffs are also responsible for jails and courts.  Cities do not maintain their own jails.  A jail falls under the responsibility of the county Sheriff.  

The job can be much the same, unless you work for a Sheriff in the courts or jail, and Deputies and Police often work together and back each other on calls.  In my experience, having worked in both a police department and now currently for a sheriff's office, it seems like Deputies have a wider variety of calls and experiences.  I deal with everything from domestic disputes to loose horses country roads, Mexican cartels growing marijuana in the mountains to mountain lions stalking hikers.  Because we patrol such a large area, the types of things we deal with can be very different than what police officers see in a city.