I would consider these words to be synonymous. Their dictionary definitions are pretty much identical:
"Unable to be explained by current science and the known natural world."
Of course, in culture and in practice, words often gain very unique connotations.
So, I'm curious (and although I imagine if you strictly believe these words are not interchangeable, that you forgive others interchanging them as they are so closely related), do you feel it's proper or not proper for them to be interchanged?
And, if the latter, please explain below how you feel the words differ in meaning or use.