Moral duties and rights

Are moral duties derived from moral rights, or vice versa? Or maybe these are two different things altogether? That is, does my moral prohibition to kill stem from the fact that others have a right to life, or does the fact that I have a moral duty not to take anyone’s life mean that everyone has a right to live? Or maybe I have both a moral duty and others have a right, but if so, what is the difference between them?
thanks