Chicago Style and Turabian Style are used interchangeably but are basically the same. Turabian is a simplified version of Chicago Style meant for students doing papers and work for classes (what we do here at MPC) and the book is much shorter. Chicago is more geared towards the writing of professional academic journal articles and books and the Chicago Manual of Style is huge! These two books, though they seem different, are both considered Chicago Style.
There are two versions within Chicago/Turabian. There is the Notes and Bibliography version that uses footnotes at the bottom of pages, and the Author-Date version that uses intext citations (like MLA and APA do). If your professor wants you to use Chicago/Turabian, check to see which version they want you to use. There are two other tabs at the top of this page, one for each version.