Chicago is the style manual of the University of Chicago Press. This manual is used by many publishers, editors, and professors throughout the English-speaking world as a guide to manuscript preparation. Note: The Chicago Manual of Style allows for two styles: Notes-Bibliography (usually used in natural and social sciences) and Author-Date (usually used in the humanities). Ask your instructor which style you are expected to use.
Turabian is an abridged version of the Chicago Manual of Style written for college and high school students. It includes more information about formatting papers and the research process than the Chicago manual. If you can't find a citation format for a source in Turabian, look in the Chicago manual.