'Natural rights' are the entitlements we feel that we have, derived from the rules we feel others must follow according to natural law. 'Natural law' is the rules for social conduct which are baked into our genes. Or, as wikipedia puts it
> Natural rights are those that are not dependent on the laws or customs of any particular culture or government, and so are universal, fundamental and inalienable (they cannot be repealed by human laws, though one can forfeit their enjoyment through one's actions, such as by violating someone else's rights). Natural law is the law of natural rights.
Natural law and natural rights are two sides of the same coin.
If natural law is a form of genetic determinism, as you suggest, genetic variation and diversity would lead to not one singular set of natural laws, but a spectrum of them. Collectively-held rights cannot be derived directly from this broad spectrum; natural rights serve as a medium through which felt natural law may be applied practically and collectively. It is thus wrong to speak of "natural law" as a justification for socially-permissible action; you are only doing as you wish, with no regard for how others feel.
Again, when you do so, you must understand that others have no obligation to tolerate it.
'Natural rights' are the entitlements we feel that we have, derived from the rules we feel others must follow according to natural law. 'Natural law' is the rules for social conduct which are baked into our genes. Or, as wikipedia puts it
> Natural rights are those that are not dependent on the laws or customs of any particular culture or government, and so are universal, fundamental and inalienable (they cannot be repealed by human laws, though one can forfeit their enjoyment through one's actions, such as by violating someone else's rights). Natural law is the law of natural rights.
Natural law and natural rights are two sides of the same coin.