It seems to me that God’s providence, or simply ‘Providence’, is neither of those, or at least it is indistinguishable from the latter for the nonbeliever (hence the utility of the term ‘hypernatural’ for believers – at least a couple of us, anyway 
).
Some occurrences, frequency of occurrences or several occurrences in sequence can be remarkable and meaningful enough to defy ‘normality’. (I did not say, ‘remarkable enough to defy nature’. ) Rich Stearns relates just such a sequence of multiple unaccountable ‘coincidental’ events in his best-selling book, The Hole in Our Gospel, that influenced him to resign from being the CEO of Lenox, Inc., manufacturer of high-end dinnerware, to become the president of World Vision, a large Christian NGO dedicated to caring for children and improving their lives. Improving their lives with basics of course, but also longer term, like giving sewing machines and training to mothers to become providers and entrepreneurs, or wells and long distance supply piping to isolated communities, as well as follow-through, equipment maintenance and training. (As a septuagenarian, I have multiple enough instances and several sequences of my own – or rather, that were given to me – that I took to documenting them in a ‘Co-instants Log’ about three and a half decades ago, with retrospective entries for two decades before that.)