Of course there are distinction.
Natural relate to nature, which doesn't defy the law of nature. Natural can be explained without resorting to explanation of god(s) or magic.
Supernatural is that of make-believe or that of simply ignorant superstition.
Anything that involved god, spirit or magic would fall under supernatural, things that totally defy nature or the law of physics. Also supernatural is the so-called miracles.
There are nature in which we can't explain or cannot yet explain, but that doesn't make it automatically "supernatural".
It is quite possible to explain what someone or something to be "supernatural".
So in reality, something that can or cannot be explained, don't mean much in regarding to natural/supernatural.
The distinction between natural and supernatural, would better to distinguish what is or isn't real -
- Natural being "real".
- Supernatural being "not real".