Question

Are moral duties derived from moral rights, or vice versa? Or maybe these are actually two different things altogether? In other words, does my moral prohibition against murder stem from the fact that another person has a right to life, or is it that because I have a moral duty not to take anyone's life, it follows from that that everyone has a right to live? Or perhaps I both have a moral duty and the other person has a right, but if so, what practical difference is there between them?
Thank you