(1) Gives the meaning of the term, the necessary and sufficient conditions of its application
(2) It is, or may be treated as, analytical (i.e., merely provides an analysis of a complex concept)
(3) Does not serve as the basis of valid generalizations
(4) Can be given of nonexistents, such as privations
(5) Can be given of nonentities, such as chimeras
(1) Identifies the essence of the thing, describes what it is for that kind of thing to be the kind of thing it is
(2) It is not analytical, but has to be discovered
(3) Serves as the basis of valid generalizations
(4) Cannot be given of nonentities, such as privations
(5) Cannot be given of nonexistents, such as chimeras
(1) For example, the term "diamond" may be said to apply to all and only those things that are colorless precious stones capable of scratching glass. Indeed, we may even say that this is all and only what we mean by the term "diamond". Still, it is not its being a colorless gemstone capable of scratching glass that makes a diamond a diamond. For a diamond would still be a diamond if there were no light to manifest its color, if there were no humans to value it and there were no glass for it to scratch. Well, perhaps, if we take it seriously that what we mean by the word "diamond" is neither more nor less than what we mean by the phrase: "colorless precious stone capable of scratching glass", we can also say that what we actually call a diamond under such circumstances could not properly be called so, there being no humans in the first place, to call it anything. Nevertheless, the fact remains that what we now identify as a diamond under this description would still be the same thing, and, indeed, the same kind of thing even under such circumstances. And this would be so precisely because this thing, insofar as it exists, retains its essential characteristics, what make it into what it is, but which are not identified in the above-mentioned description. A definition probably successfully identifying these essential characteristics would be the following: "a diamond is a piece of tetrahedrally crystallized carbon". Provided this is indeed a successful identification of the thing's essence, this description would apply to a diamond even under the above-mentioned circumstances in the sense that the properties attributed to it by this description would still be present in it, even if there were nobody to identify them as such.
(2) The first definition of the term "diamond" is certainly analytical, provided we hold that this is precisely what we mean by this term, come what may, for in this case we would not call anything a diamond except when it has precisely the characteristics mentioned in this description. By supplying this definition, then, we only explicate what we think is involved in our concept of a diamond, i.e., what should apply to a thing in order that we call it a diamond, and we do not care whether this concept and the involved characteristics are indeed essential to the thing or not. To be sure, as we could see above, it is possible to imagine a situation in which what we actually call a diamond does not have the characteristics implied in this definition (precisely because these characteristics are accidental), but this would not falsify the definition, for in such a case the thing simply would not fall any longer under our actual (complex, accidental) concept of a diamond. So it would still be true that what we call a diamond is such as it is described in its nominal definition, and so we can always know that a diamond is such, regardless of what happens to the thing, and what we may experience.
On the other hand, if the other definition does indeed succeed in identifying the essence of diamonds, then it cannot be the case that the thing, while remaining what it is, indeed, simply remaining in existence, does not have the characteristics mentioned in this definition. But this is not something that we can find out about a diamond by simply analyzing our (complex, accidental) concept of a diamond, trying to identify the necessary and sufficient conditions of its application. It is probably a genuine discovery for anyone, long after being able to apply properly the term "diamond", that the precious thing that goes by that name is after all the same material that one has in one's pencils, for example, but with a different molecular structure.
(3) The fact that the thing retains its essential qualities under any circumstances under which it remains in existence at all renders real definitions the basis of valid, non-trivial generalizations. On the basis of the real definition of diamonds we can predict the properties of any diamond under any possible circumstances under which it exists, indeed, we can even tell what are the conditions, say, what temperature, under which it cannot exist.
This is not the case, however, with nominal definitions. Since the nominal definition of a term simply helps us to identify the properties which a thing should have so that the term will apply to it, but these properties may be accidental to the thing, it may well be the case that the same thing in certain circumstances does not have these properties, whence it does not fall under the same term. So even if it is necessary that whatever is a diamond is a precious stone capable of scratching glass, it may be the case that what actually is a diamond in some possible situation does not have these properties, i.e., what is a diamond may not be a precious stone capable of scratching glass. But then, this definition does not tell us anything about the behavior of the thing it actually applies to in several possible situations as the real definition does, but only tells us about the circumstances under which the term simply would not apply. Hence, the nominal definition does not enable us to make valid, non-trivial generalizations as to the behavior of the things it actually applies to in all possible situations at all times as the real definition does.
(4-5) A further consequence of the above considerations is that real definitions can be given only of things that have real essences. For a real definition signifies a thing's essence. But then a thing that does not have an essence cannot have a real definition. A thing that has no essence is an object of thought that does not have any real existence in external reality, still the mind can conceive it, and signify it. But then the name signifying such a thing certainly can have a nominal definition saying what we mean by the name, what we intend to signify, whether successfully (as in the case of privations) or not (as in the case of figments in non-ampliative contexts).
"Sicut quid rei est quidditas rei, ita quid nominis est quidditas nominis: nomen autem, cum sit nota earum quae sunt obiective in anima passionum (ex primo Perihermeneias), non habet aliam quidditatem nisi hanc, quod est signum alicuius rei intellectae seu cogitatae. Signum autem ut sic, relativum est ad signatum: unde cognoscere quid nominis nihil est aliud, quam cognoscere ad quid tale nomen habet relationem ut signum ad signatum. Talis autem cognitio potest acquiri per accidentalia illius signati, per communia, per essentialia, per nutus, et quibusvis aliis modis. Sicut a Graeco quaerentibus nobis quid nominis anthropos, si digito ostendatur homo iam percipimus quid nominis, et similiter de aliis. Interrogantibus vero quid rei oportet assignare id quod convenit rei significatae in primo modo perseitatis adaequate. Et haec est essentialis differentia inter quid nominis et quid rei, scilicet quod quid nominis est relatio nominis ad signatum; quid rei vero est rei relatae seu significatae essentia. Et ex hac differentia sequuntur omnes aliae quae dici solent: puta quod quid nominis sit non entium, complexorum, per accidentalia, per communia, per extranea; quid rei vero est entium incomplexorum per propria et essentialia. Relatio enim vocis potest terminari ad non entia in rerum natura, et complexa, et declarari per accidentalia et huiusmodi, essentia autem rei non nisi per propria essentialia habetur de entibus incomplexis. [Thomas de Vio Cardinalis Cajetanus: Super Librum De Ente et Essentia Sancti Thomae, in: Opuscula Omnia, Bergomi, Typis Comini Venturae, 1590, p. 290.]
"Just as the quid rei is the thing's quiddity, so the quid nominis is the quiddity of the name: but a name, as it is the sign of the passions that are objectively in the soul (from bk.1. of Aristotle's Perihermeneias), does not have any other quiddity but this, namely that it is a sign of a thing understood or thought of. But a sign, as such, is a relation to what is signified: so to know the quid nominis is nothing, but to know what the name, as a sign, is related to, as what is signified. Such a knowledge, however, can be acquired by the accidental properties of what is signified, as well as by its common, or by its essential properties, or simply by a gesture, or whatever else you like. For example, if we ask a Greek about the meaning of anthropos, if he points to a man, at once we know the quid nominis, and similarly in other cases. But to those asking about the quid rei, it is necessary to give what belongs to the thing in virtue of its essence. This is the essential difference between the quid nominis and the quid rei: namely, that the quid nominis is the relation of the name to what it signifies; but the quid rei is the essence of the thing related or signified. And it is from this difference that all the rest that are usually enumerated follow: namely, that the quid nominis is of nonentities, complexes, by accidental, common, and external properties; while the quid rei is of incomplex entities [grasped] by their proper, essential properties. For a word's relation can be terminated to non-existents, and it can be clarified by accidental and similar properties, but the thing's essence can be known only by proper, essential properties of incomplex things."