What differentiates hard evidence from circumstantial evidence? It comes down to the probabilities, which in turn comes down to statistics.
Circumstantial evidence is evidence which requires a logical inference in order to support the point for which it is introduced.
That is roughly how evidence is explained by judges to juries in courtrooms.
For example, the victim's blood on the defendant's shoe is noncircumstantial evidence because it directly supports the point that the defendant was present in the vicinity of the victim's body. However, finding at the crime scene a brown fiber which is same type of fiber used to stich the defendant's very expensive, limited edition gloves, would be circumstantial evidence because you have to logically infer that the fiber found comes from the defendant's gloves. Alternatively, finding gloves that are identical to the defendant's gloves is also circumstantial evidence unless there is other evidence showing conclusively that those particular gloves are the defendants, i.e., footage of the defendant leaving the gloves there or something.
The difference between the probabilities involved in the above inferences, and the analogous inferences ineluctably underlying any hard evidence, and those involved in circumstantial evidence like your coat fiber, are purely quantitative. In some sense, hard evidence is that which can be accepted "beyond a reasonable doubt", while circumstantial evidence is that which does not pass such a test.
Unfortunately, "beyond a reasonable doubt" escapes precise definition. Yet, courts need to function, so we tacitly agree that sufficiently large quantitative differences are (legally) indistinguishable from qualitative differences.
(EDIT: I'm saying the same thing as mikeash, whose response appeared while I was writing my own)
Noncircumstantial evidence directly supports the point for which it is introduced if the evidence is what it claims to be. The victim's blood on the defendant's shoe directly supports the point that the defendant was in the victim's presence when the victim was dying if it is established that the blood is the victim's blood.
Circumstantial evidence requires an additional inference beyond this step. The fibers are circumstantial because the fiber doesn't prove anything except that the someone wearing those gloves might have been at the crime scene at some point in time. You require the additional inference that the fiber was left at the scene at the time of the crime, which the fiber by itself does not prove but which can be "circumstantially" proved in combination with other evidence. For example, if the defendant, or some other witness, claims that the defendant was never at the scene of the crime at any point in time (specifically, but not limited to, periods prior to the crime), the presence of the rare fibers from his rare gloves is circumstantial evidence that the only time he was at the scene of the crime was when the crime occurred. In other words, the circumstances surrounding the fiber are the proof, not the fiber itself.
The (admittedly pedantic) point being made is that proving 'x' never directly supports anything other than the truth of 'x'. Moving from 'x' is true to 'y' is true always requires further inference.
However, the main point of this thread of discussion I think was that even things that legally are considered "direct evidence" - say, testimony of an witness to the crime - do nonetheless involve some inference...
Circumstantial evidence is indirect, like you being in the area of something, hard evidence is actually of you committing an alleged act.