Q. What's the difference between Chicago Notes and Bibliography and Author-Date styles?
Chicago has two versions based on the type of research being done. The Sciences and Social Sciences often use Author-Date style, which uses parenthetical in-text citations with a references list at the end of a paper. The Arts and Humanities often uses Notes-Bibliography style, which relies on footnotes or endnotes with a bibliography at the end of a paper.
If you are unsure what version of Chicago to use, consult with your professor.