The Chicago Manual of Style presents two basic documentation systems: (1) notes and bibliography and (2) author-date. Choosing between the two often depends on subject matter and the nature of sources cited, as each system is favored by different groups of scholars.
The notes and bibliography style is preferred by many in the humanities, including those in literature, history, and the arts. This style presents bibliographic information in notes and, often, a bibliography. It accommodates a variety of sources, including esoteric ones less appropriate to the author-date system.
The author-date system has long been used by those in the physical, natural, and social sciences. In this system, sources are briefly cited in the text, usually in parentheses, by author’s last name and date of publication. The short citations are amplified in a list of references, where full bibliographic information is provided.
Source: The Chicago Manual of Style Online