Chicago Style and Turabian Style are two very similar citation styles. Both are manuals from the University of Chicago Press. Chicago Style refers to the citation style developed in the book Chicago Manual of Style. Turabian Style is from the the book A Manual for Writers of Research Papers, Theses, and Dissertations by Kate Turabian, a dissertation secretary at the University of Chicago for over 30 years. Both styles are commonly used for papers in the social sciences.
Chicago Style presents two basic documentation systems: 1) Notes & Bibliography OR 2) Author-Date References. Writers must choose one of these formatting styles and stick with it. Choosing between the two often depends on subject matter and the nature of sources cited, as each system is favored by a different group 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 (from the Chicago Manual of Style Online).
Turabian Style, commonly referred to as just "Turabian," is based on Chicago Style, but omits some of the publishing details and options in the Chicago Manual of Style. Turabian is more focused on the most important rules for student papers and other scholarly research not intended for publication.
Note: A new version of the Chicago Manual of Style was published in 2017. If you're using a guide that's based on the 16th edition of the Chicago Manual of Style, please consider comparing it to the 17th edition to ensure you're using the correct formatting.