What is the difference between Chicago and Turabian?
The primary difference is that Turabian is shorter and contains fewer instructions and that it does not contain information about the publication. The Chicago Manual of Style is designed for professionals in the field who are publishing and has a great deal of instruction on formating and many other things. Turabian is a pared-down version designed for students writing research papers.
Which should I use?
You should always talk to your professor or librarian, but for the most part, all of the guidelines that you find in Turabian help pages will also apply to the Chicago style.