The essential difference between natural and positive law can be summed-up by a brief examination of Sir Leslie Stephen's famous remark in The Science of Ethics:
If a legislature decided that all blue-eyed babies should be murdered, the preservation of blue-eyed babies would be illegal.
Positive law is whatever the legislature says it is (or, in jurisdictions where case law is binding, whatever the judiciary has ruled in cases which have not been overturned and constitute sources of precedent). It is the sum total of all statutes and case law operating in a given place at a given time. If this includes a law necessitating the murder of blue-eyed babies, that law is as valid as any other.
Natural law is law which claims a basis in God, nature or reason. It could not, therefore, include the murder of blue-eyed babies, whatever the statues happen to say. According to the idea of natural law, rights are not conferred by statute but are inherent.
It is generally assumed, as Aristotle assumed, that in a society governed by the rule of law rather than by tyranny, positive and natural law will coincide, since a positive law which was manifestly contrary to natural law would never be passed by a legislature (and if it were passed, citizens would see no reason to obey it). In practice, however, conceptions of natural rights differ considerably between societies, so some of the positive law in any country will be certain to seem unjust (and therefore contrary to natural law) to many people. This applies in particular to laws regarding such matters as controlled substances or freedom of religion, about which there is little international agreement.