Definition of supernatural | Dictionary.com
Looking at the 1st couple definitions...
adjective
1) of, relating to, or being above or beyond what is natural; unexplainable by natural law or phenomena; abnormal.
2) of, pertaining to, characteristic of, or attributed to God or a deity.
Definition of naturalism | Dictionary.com
Looking a the philosophical definitions...
4) Philosophy.
a) the view of the world that takes account only of
natural elements and forces, excluding the supernatural or spiritual.
b) the belief that all phenomena are covered by laws of science and that all teleological explanations are therefore without value.
These strike me as fitting common usage pretty well.
But problems could arise if (as the OP suggests) ghosts are
discovered, & they could be studied by scientific means.
Formerly considered supernatural because they were untestable,
they'd enter the realm of science. But until this hypothetical
musing becomes real, we've a clear division with ghosts in the
supernatural, but not in the natural world.