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In Scholastic logic, differentia is one of the predicables. It is that part of a definition which is predicable in a given genus only of the definiendum; or the corresponding "metaphysical part" of the object.
Origin of the notion
The concept of differentia was, as a matter of fact, already employed by Plato when he conceived his method of diairesis. Aristotle used the term diafora in a systematical fashion; but he had no explicit theory about it and his understanding of the term is controversial. A theory was only provided by Porphyry's explicit treatment of the predicables presented in his Isagoge. On the basis of Boethius' translation of the Isagoge, where the Greek term diafora was rendered as in Latin as "differentia", evolved the elaborate Scholastic theory of the predicables.
In the original, logical sense, a differentia is a kind of concept - so the notion of "differentia" is a second-order concept, or a "second intention", in the Scholastic nomenclature. In the scholastic theory it is a kind of essential predicate - that is, a predicate which belongs to its subjects de re necessarily. It is distinguished against the species by expressing the (specific) essence of the object only partially, and against the genus by expressing the determining rather than the determined part of the essence.
Although the primary meaning of "differentia" is logical or second-order, it may under certain assumptions have an ontological, first-order application. If it is assumed that the structuring of an essence into "determining" and "determinable" metaphysical parts (which corresponding to a differentia and a genus respectively) exists in reality independently of its being conceived, one can apply the notion "differentia" also to the determining metaphysical part itself, and not just to the concept that expresses it. This is common in Scotism, where the metaphysical parts are said to be formally distinct. If, on the other hand, any mind-independent structuring on the part of the essence is denied (like in Thomism or Suárezianism), then the partitioning of the essence into a generic and a differentiating part must be considered as merely conceptua, whereas the actual realities corresponding to the differentia and to the genus evade as really the same. These assumptions therefore do not permit any ontological application of the notion of differentia.