A County "Sheriff" in most (all?) states is a State Constitutional Officer and an elective (as opposed to an appointive) position.
The Sheriff (and his deputies) have the power to enforce BOTH the criminal AND the civil statutes of the state, whereas 'police' departments may only enforce criminal law.
A Sheriff possess wide powers under the state constitution and is considered to be the the chief law enforcement officer of the entire county, regardless of whether the individual municipalities within the county have their own chiefs or not. His power exceeds and supersedes theirs when he wishes to exercise it.
A "Deputy Sheriff" is simply the title/rank of those who the Sheriff chooses to "deputize" and who carry out the duties of the Sheriff's office, which in today's world are many and varied (e.g.: operation of the jails - court and judicial security - service of court papers - uniformed patrol - etc - etc). Deputies also can exercise their authority anywhere in their entire county and may take law enforcement action regardless of what municipality they may be in.
The Roy Rogers Show - 1951 The Deputy Sheriff 3-12 was released on: USA: 7 February 1954
it takes 4 months to be a cop
Deputy Dingle - 2009 1-3 was released on: USA: 12 September 2010
Deputy Dingle - 2009 was released on: USA: 3 March 2009
The Deputy - 1959 Back to Glory 1-3 was released on: USA: 26 September 1959
Maverick - 1957 The Sheriff of Duck 'n' Shoot 3-3 was released on: USA: 27 September 1959
Dodging the Sheriff - 1912 was released on: USA: 3 February 1912
Even Later with Salvatore Rizzo - 2011 Even Zombies Know Being Stiff Has Its Advantages 1-3 was released on: USA: 23 October 2011
(3) Depp-you-tee.
The People's Choice - 1955 The Sheriff 3-16 was released on: USA: 16 January 1958
Sheriff of Cochise - 1956 The Dude 3-8 was released on: USA: 4 October 1957
Sheriff of Cochise - 1956 The Crow 2-3 was released on: USA: 24 July 1957