A conspiracy theorist is someone who has a theory and tries to find data to support it (lets call this “positive data”) while marginalizing and/or ignoring any data which falsifies it (“negative data”). When the evidence used to maintain a theory is falsified, a conspiracy theorist will either deny the evidence (see below) or move on to find new – and usually more and more arcane and obscure – evidence that supports it while retaining a positive belief in his theory based on faith until he finds it. A main characteristic of the conspiracy theorist is that the evidence which falsifies his theory will not make him reconsider the validity of his theory itself but rather make him strive to find new positive data instead.
Example is the 9/11 truther movement which sees various evidence of planned demolition of the twin towers (such as exploding windows, burning steel etc) but refuses to acknowledge the evidence of internal collapse and the information that explains burning steel and so on.
The same tactics are also used by Woo-Woo peddlers as well as the religious.
A denialist is someone who does not like a theory and is thus trying to find data which falsifies it. However he has a conspiracy theorist outlook on selecting them. I.e. In order to prove his falsification theories, he tries to find data to support them while ignoring those that refute them and constantly replaces negative data as previous ones are debunked.
Unlike a skeptic (see below) who considers various ways to falsify a theory as well, a denialist will refuse to acknowledge a theory when it withstands all falsifications. Whereas a skeptic will gladly accept a theory he (or the relevant expert consensus in the field) can’t prove wrong until such time as new evidence comes to light that falsifies it, a denialist will retain that the theory is wrong, no matter the evidence. As such, occasionally a denialist may run out of negative data but retain his denial on faith alone, while constantly trying to discover some shred of evidence, no matter how obscure, to grasp onto.
Example is the Anthropogenic Global Climate Change Denialist movement (that’s a mouthful) who’s been jumping from evidence to evidence to support their denial, while ignoring the mass of positive data for AGCC has accumulated and not considering the significance of all the falsification theories they used to espouse before they were debunked in turn.
A skeptic is someone who sees a theory that does not fit with the current collective knowledge of humankind (i.e. science) and look for ways prove such a theory wrong before accepting it. A theory will only be accepted when it cannot be falsified. However a theory that can bears no falsification (such as an afterlife) can be ignored when it has no corresponding positive data, as it is of no material consequence. For example, “All humans are mortal” is unfalsifiable but also unimportant as is “Some humans are immortal”. Unless one can show who is immortal and why, the validity or not of such a theory is irrelevant as long as we can accept that by overwhelming evidence, all humans are mortal.
Similarly a proposition such as “afterlife exists” or “ghosts exist” are irrelevant to a skeptic unless positive data can be brought to light to show how those proposition might be true. Once such evidence is brought to light, a skeptic will try to falsify them in order to avoid deluding himself. Only if those theories survive falsification will they be accepted.
A skeptic also recognises that it’s impossible to be knowledgeable in all sectors of human knowledge and is content to defer to experts who have studied each scientific area. As long as there is a consensus of scientists in a given area, a skeptic who has neither the knowledge or the time to acquire it, is justified in relying on scientific consensus. However this is only an acceptable practice for skeptics who recognise their limitations, not a way of doing science. As such, a skeptical expert of a scientific area is within her rights to challenge a theory which has the consensus of her peers and attempt to falsify it when new evidence comes to light. In fact, I would say this is her duty.
In short, the primary difference between a skeptic and a conspiracy theorist is that the skeptic gives far more weight to the falsification of a theory rather than the evidence for it. The primary difference between a skeptic and a denialist is that the skeptic accepts a theory he or the scientific community cannot falsify which is also supported by positive data. The difference with both, is that a skeptic will be neutral towards a theory at the start, unlike starting positive to it like the Conspiracy theorist or negative to it like the Denialist based on some kind of gut feeling. A skeptic will become positive to a theory only when there is overwhelming evidence and/or consensus for it and negative to it when there is overwhelming falsification and/or no evidence for it.
On the other hand, the reason why so many denialists are also conspiracy theorists is because their methods complement each other. A conspiracy theorist would have a problem maintaining his theories if he did not consistently deny the evidence against them and a denialist would have a problem sustaining his denial if he did not avoid reconsidering his opposition when his evidence failed. As such, it’s easier for a denialists to be taken in by conspiracy theorists (think of those AGCC denialists who blame the scientific consensus to a global New World Order cabal) and conspiracy theorist or woo-woo peddlers are very likely to turn into denialists against theories which run counter to their conspiracy theories.