Turabian is "a style of writing and formatting that is created and updated by Kate Turbian. It is adapted from the University of Chicago's 'Chicago' style of citation and is simplified for students and researchers. Turabian is most commonly used in the social sciences, such as in History courses" (thanks to Muskingum University's Turabian Libguide).
While the two styles are very similar, they do have differences, you should always check with your professor to see which you should be using, and follow suit. The Chicago style is used often for professional publication and if you are in an upper level or graduate level class, your professor may well hope you aspire to professional publication, and expect you to use Chicago style