There are three types of paradox:

Paracosmia. If the reasoning is faultless and the source of the contradiction lies in the bringing together of two incompatible realities, then we’re dealing with a cognitive paradox, a paracosmia (e.g. Olbers’ “sky on fire”, which contradicts the fact that the sky is black at night). This is the type of paradox that has always flourished in the sciences, so much so that they are often referred to as scientific paradoxes.

Paralogy. If the incompatible realities presented are irrefutable, but specious reasoning is the cause of the contradiction, we’re dealing with a logical paradox, a paralogy (e.g. Socrates is mortal, a horse is mortal, therefore Socrates is a horse). The apparent demonstration that leads to the contradiction has in fact not taken place. While paralogy is an error of reasoning (a logical error), sophistry, which is also an error of reasoning, is distinguished by its intention to deceive.

Paradoxy. If the realities presented and the reasoning are all correct, but no reasonable conclusion can be reached, then we can speak of a paradoxy, or a logical dilemma, or even antinomies (e.g. the paradox of the Liar or the Barber).