"[T]he first of Chicago's two systems of source citation . . . uses notes, whether footnotes or endnotes or both, usually together with a bibliography. The notes allow space for unusual types of sources as well as for commentary on the sources cited, making this system extremely flexible. Because of this flexibility, the notes and bibliography system is preferred by many writers in literature, history, and the arts" (CMOS 14.2).
"The author-date system is used by many in the physical, natural, and social sciences and is recommended by Chicago for works in those areas. Sources are cited in the text, usually in parentheses, by the author's last (family) name, the publication date of the work cited, and a page number if needed. Full details appear in the reference list usually titled 'References' or 'Works Cited' "(CMOS 15.5).