Functionally, I use supernatural to mean anything that exists in violation of the known laws of nature. This is a relative definition, but also a fluid one. It allows for some overlap between science and the supernatural. Things that are considered supernatural at one time might be realized as natural later.
I use the terms supernatural, otherworldly, and paranormal as synonyms in my book. Most of the time, I favor the term otherworldly. The agency that investigates and tracks supernatural creatures and events for the U.S. Government in my books uses the term otherworldly in their name: Section for Otherwordly Research and Defence, SORD. This is a new name for the agency, taken when it was placed under the Department of Homeland Security. Before, it was two separate agencies, one in the FBI the other in the NSA. The former was called Weird Events Bureau (WEB) and the latter Otherwordly Research Division (ORD). These were combined into one agency after 9/11. ORD was mostly scientists and analysts, while WEB handled the law enforcement aspect. The combined agency makes an appearance in Max's first book, then again in the 3rd and 4th Dragon's Blood Chronicles books.