United States Marshal

A United States Marshal, or just Marshal, was a law enforcement title held by some Americans. The First Doctor, Steven and Dodo once met the Marshals of Tombstone, Arizona and Dodge City, Kansas. (DW: The Gunfighters) The Eleventh Doctor himself was once temporarily appointed a Marshal in Mercy, Nevada in 1870. (DW: A Town Called Mercy)

Behind the scenes
As may be expected of a British television programme, understanding on the intricacies of American law enforcement aren't well represented in Doctor Who. Little was explained in either televised as to what a Marshal actually was, or how the position differed from that of Sheriff. However, both Donald Cotton and Toby Whithouse chose to stress the fact that their lawmen were Marshals, not Sheriffs.

Though many non-Americans assume that "Marshal" is a somewhat archaic name that is most associated with the 19th century West, in fact the US Marshal Service dates to the 18th century and is still a vital part of the American legal system in the 21st.

The main job of a Marshal is to protect and serve the Federal Judicial districts, while truly local law enforcement officials, like Sheriffs and city police officers, are more directly accountable to the people within the area they serve.

Since Marshals aren't elected — and Sheriffs are — it was more-or-less accurate for Isaac to appoint the Eleventh Doctor a Marshal in A Town Called Mercy — given that the dying lawman had few other options to maintain the continuity of his office.