No, publicity rights are a branch of state tort law. Copyrights are a sui generis branch of federal law.
And a copyright release is just a copyright license (or more rarely, an assignment), which means that it pertains to a particular creative work. A publicity release has to do with using someone's face, image, statements, etc. While you could conceivably have them both in the same form, it's rare that you'd need to or want to.
And I assure you, they are not related even the teeniest tiniest bit. Not in their policy goals, or how they originated, or which governments created them, or who gets them, or how long they last, or what they cover. There is no commonality.
Are you too lazy to google for the difference between copyrights and publicity rights? Perhaps this web page from the Library of Congress will help you out: http://memory.loc.gov/ammem/co...