The Chicago and Turabian styles are one and the same. Kate Turabian's Manual for Writers is simply the University of Chicago format adapted for student use.
Chicago/Turabian recognizes two methods of citation. Be sure you know which method your professor wants you to use:
The notes-bibliography style (N.B.) is commonly used by writers in the humanities. This unique Chicago style uses footnotes (or endnotes), which allow the writer to include commentary.
The author-date style, or "parenthetical citation-reference list" style (P.R.), is used in the natural and physical sciences, as well as some social sciences.