There were several unrelated Derby labels in the United States and internationally:
Derby Records (1950s) was founded in the late 1940s in New York City. The label offered selections in various styles of pop music of the era, including Rhythm and Blues and Western swing. As far as we know, no longplay albums were released on this Derby label until it folded in the early 1960s.
Derby Records (1960s) was a subsidiary of Sam Cooke's SAR Records, founded in 1963. Only two albums were released on this Derby label, one by Mel Carter and the second by Billy Preston. As Preston had also recorded for the previous Derby label, and both these American labels featured a derby hat on the logo, we are not entirely sure that there really was no relation between these two. After Sam Cooke was murdered in 1964 his widow closed both SAR and Derby Records.
Derby Records (Italy) was established in 1962 as the international division of Compagnia Generale del Disco (CGD). In the mid-1970s the label became one of the most important early Disco labels in Italy. And the end of Disco also meant the end for Derby; it was closed in 1982.