I think 'supernatural' is used explicitly to refer to things
which defy natural explanation ... but it is almost
impossible to differentiate between 'super' and 'praeter'
natural (the latter meaning not yet understood, while the
former means without natural explanation).
Many supposed super-natural phenomena, if accounts are taken
at face value, are most likely explainable with sufficient
study.
In the context of this forum, I beleive supernatural tends to
be used to refer to the workings of an intelligent, omnipotent
agency who is not confined by the natural 'laws' that govern
the rest of us.