The supernatural (Medieval Latin: supernātūrālis: supra "above" + naturalis "nature", first used: 1520–30 AD) is that which is not subject to the laws of physics or, more figuratively, that which is said to exist above and beyond nature.
The supernatural is a feature of the philosophical traditions of Neoplatonism and Scholasticism. Most religions include the supernatural, and it is also a feature of the paranormal and occultism. (wiki)
In philosophy, naturalism is the "idea or belief that only natural (as opposed to supernatural or spiritual) laws and forces operate in the world."Adherents of naturalism (i.e., naturalists) assert that natural laws are the rules that govern the structure and behavior of the natural universe, that the changing universe at every stage is a product of these laws.
"Naturalism can intuitively be separated into an ontological and a methodological component." "Ontological" refers to the philosophical study of the nature of reality. Some philosophers equate naturalism with materialism. For example, philosopher Paul Kurtz argues that nature is best accounted for by reference to material principles. These principles include mass, energy, and other physical and chemical properties accepted by the scientific community. Further, this sense of naturalism holds that spirits, deities, and ghosts are not real and that there is no "purpose" in nature. Such an absolute belief in naturalism is commonly referred to as metaphysical naturalism.
In contrast, assuming naturalism in working methods, without necessarily considering naturalism as an absolute truth with philosophical entailments, is called methodological naturalism. The subject matter here is a philosophy of acquiring knowledge.
With the exception of pantheists—who believe that Nature and God are one and the same thing—theists challenge the idea that nature contains all of reality. According to some theists, natural laws may be viewed as so-called secondary causes of god(s).
In the 20th century, Willard Van Orman Quine, George Santayana, and other philosophers argued that the success of naturalism in science meant that scientific methods should also be used in philosophy. Science and philosophy are said to form a continuum, according to this view. (also Wiki)
Supernaturalism brings no enlightenment to anything. It's primary useful function (at least as I observe it) is it's use in impressing impressionable and vacuous new-age coeds.
Naturalism, on the other hand, leads to models that make consistent and accurate predictions about the universe and it is need for everything from landing people on the Moon to fighting Ebola on the Earth.