The problem of the generic colloquialism "thriller" is indeed a tough one. As an actual name for a genre "thriller" is pretty much useless, for even a glance at Wikipedia gives one of a cornucopia of subtypes-- action-thriller, horror-thriller, erotic thrillers-- that wander all over the genre-map. However, the debate between B-Sol and Merilyn Merlot isn't concerned with any subtypes that aren't directly related to horror. B-Sol's suggestion of a divide between natural/supernatural is an attempt to find a dividing line between the pure horror film and what Wiki would probably have termed the "horror-thriller," as per some of the examples discussed, like JAWS and THE SILENCE OF THE LAMBS.
Parenthetically let me suggest a different term in place of the scattershot colloquialism "thriller." I used said term in this essay earlier:
In some ways, THE HAPPENING shares elements of both horror and suspense films. The idea of city-dwellers thrown into a mammoth catastrophe evokes the suspense-oriented narrative of the disaster film, with a side-dish of terrorist-fantasy flavoring. However, the theory about the source of the malady is presented in so oblique a way that it partakes less of the well-defined threats of a suspense-film and becomes more of a *mysterium*
The "suspense" genre, I said in a related post, was oriented not on seeking to scare the audience, but to "startle and disorient." In my own conception the pure horror film doesn't necessarily need the element of the supernatural, but it does need the element of the *mysterium,* which is my shortened form for the two Latin phrases invoked by Rudolf Otto is his classic IDEA OF THE HOLY, where he explains the numinous experience in terms of the *mysterium tremendum,* the overwhelming mystery that compels fear and trembling in the viewer, and the *mysterium fascinans,* which compels the viewer to be attracted to the fascinating mystery.
Like B-Sol, I find many non-supernatural films have enough of a "mysterioso" aspect to them that they remain conceptually within the bounds of the pure horror film. Hitchcock's PSYCHO is one example. Nothing supernatural occurs in the story, but the disintegration of Norman Bates' mind seems to be a transformation of normality as profound as if he had been possessed by a demon or the like.
However, while the horror film needs the *mysterium* in some form, the suspense film-- which is what I'd hazard is really what most people mean when they say "thriller"-- does not in general dwell on any overwhelming mysteries, as I would say is the case with both PSYCHO and the film I originally discussed in the above citation, THE HAPPENING. The Shyamalan film does have a *mysterium* at its core that aligns it with the pure horror film, but 1971's ANDROMEDA STRAIN is still a textbook example as to how to craft a suspense film that does have metaphenomenal (though not supernatural) underpinnings.
For that matter, the SILENCE OF THE LAMBS film also seems to have more in common with the suspense genre than that of horror. Hannibal Lecter is certainly mad, but it's questionable as to whether his madness is as grotesque and transformational as that of Norman Bates. Both characters inhabit essentially realistic worlds, but Hannibal's madness has far less mystery to it.
More on these matters later, probably.
ADDENDUM, 2-26-14: Just a note to myself that currently I do regard SILENCE as having its own "mysterium," albeit not one as overt as that of PSYCHO, and that therefore SILENCE does effect a "transformation of normality."