Natural law can refer to many different philosophies. Generally natural law philosophy simply posits that there is some objective set of ideal rules describing ethics, which all human beings should theoretically be able to agree upon and derive from a rational understanding of the world. Such philosophies usually start with some very small number of broad values (like "Happiness is the ultimate good." or "The interests of every person should be weighed equally.") and attempt to derive an entire system of ethics from them.
Theistic natural law
Some natural law philosophies additionally state that the "natural law" was created by God. The concept is a part of Catholic theology but generally rejected by most Protestant denominations which generally favor divine command theory.  In natural law philosophies, it is not a fallacy to claim that "natural" and "moral" are the same, because both were created by God to be consistent with each other. However, these philosophies are only viable if one can demonstrate the existence of an absolute moral law and a God that created both the natural world and that law.
Strikingly, even in this kind of natural law, it is fairly useless to say that something is wrong because it is unnatural. These philosophies define both what is "natural" and what is "good" as being whatever is in accordance with God's will towards creation. To prove that something is unnatural in this sense means to prove that it is against God's plan. But "natural" already has straightforward definitions. To add this other, more unusual definition serves no purpose except to confuse the issue and risk some form of equivocation (between a usual definition of "natural" and this unusual meaning of "according to God's plan"). One might as well ditch the word "natural" entirely and use a different word or phrase instead.
- Stephen O Sullivan and Philip A. Pecorino, Problems with Natural Law Theory, 2002