Very briefly, works in the public domain can be used by others without violating any existing copyright protections. As the U.S. Copyright Office explains: “A work of authorship is in the ‘public domain’ if it is no longer under copyright protection or if it failed to meet the requirements for copyright protection. Works in the public domain may be used freely without the permission of the former copyright owner.”
Works released with a Creative Commons license are still copyrighted materials, however, they have been released with a copyright license that allows certain types of re-use without seeking the express permission of the copyright holder. The 6 different Creative Commons licenses signal the allowable terms of reuse. Any reuse of a work release under Creative Commons requires attribution of the source and author.
NOTE: Whether you use works that are in the public domain or protected by copyright, it is always advisable to provide proper attribution for the work.