【Supernatural】 , 【supranatural】 ,  【preternatural】 ,  【miraculous】 ,  【superhuman】  are overlapping rather than strictly synonymous terms whose meanings all involve a contrast with what is natural or, sometimes, normal or predictable.

All, with the possible exception of the uncommon  【supranatural】  , are used hyperbolically to mean exceeding usual or likely human standards and then are generally equivalent to such terms as extraordinary , exceptional , or wonderful ; thus, in an emergency a man may exhibit  【supernatural】  strength; one may show  【preternatural】  awareness of small sounds when alone at night; a scholar may decipher a manuscript with  【miraculous】  accuracy; a player may win against odds by a  【superhuman】  effort.

【Supernatural】 stresses deviation from the natural that is felt as above or beyond what is observable and capable of being experienced by ordinary means; in much of its use it suggests spirituality and implies a relation to God or to divine powers, but sometimes the word loses these suggestions and implications and can then denote more or less neutrally a transcending of the natural and comprehensible or known or it can apply to things commonly felt as matters of superstition rather than of divine spirituality and then often carries a depreciatory note.

【Supranatural】  implies a transcending of what is natural and especially of what is comprehensible or capable of becoming comprehensible; it is likely to be chosen when the theistic connotations of  【supernatural】 are to be avoided.

【Preternatural】 applies chiefly to what is not regarded as natural or being within the usual range or compass of nature. Usually the term means abnormal or strange and inexplicable to an extreme or startling degree.

【Miraculous】 applies particularly to events or effects in the physical world that are out of the ordinary course of things or that deviate from the known laws of nature either in kind or degree.

In its also common religious use 【miraculous】 applies to what is regarded or accepted as performed by divine power or happening as a result of divine intervention.

【Superhuman】  is sometimes used in the sense of  【supernatural】  but in this use it tends to stress the notion of being higher than mankind or sometimes than average or ordinary mankind and it does not carry a clear implication of divinity as  【supernatural】 often does.