Chicago Manual of Style

The notes and bibliography system is preferred by many working in the humanities—including literature, history, and the arts. In this system, sources are cited in numbered footnotes or endnotes. Each note corresponds to a raised (superscript) number in the text. Sources are also usually listed in a separate bibliography. The notes and bibliography system can accommodate a wide variety of sources, including unusual ones that don’t fit neatly into the author-date system. The Chicago Manual of Style Online - Chicago-Style Citation. 

The author-date system is more common in the sciences and social sciences. In this system, sources are briefly cited in the text, usually in parentheses, by author’s last name and year of publication. Each in-text citation matches up with an entry in a reference list, where full bibliographic information is provided. Aside from the use of numbered notes versus parenthetical references in the text, the two systems share a similar style.  The Chicago Manual of Style Online - Chicago-Style Guide