The first "Sun Records" were single-sided disc records put out by the Crystalate Gramophone Record Manufacturing Company Ltd of Kent, England, from about 1905 to 1910. (The same company would later produce records under the name Imperial).
A nearly contemporous label was produced in the United States by the Leeds & Catlin company, about 1905-1907.
The fourth and most famous "Sun Records" was based in Memphis, Tennessee starting in the 1950. Founded by Sam Phillips, Sun Records was known for giving notable musicians such as Elvis Presley, Carl Perkins, Jerry Lee Lewis, and Johnny Cash their first recording contracts and helping to launch their careers. The music of many Sun Records musicians helped lay part of the foundation of late 20th century popular music and rock and roll and influenced many younger musicians, particularly the Beatles.
For a more detailed discussion see of this last Sun Records see: Sam Phillips.