Basil the Great is one of the better-known theologians of the early church. He wrote at the beginning of the post-nicene era, and did much to combat Arianism. Basil wrote a letter to his brother Gregory in which he elucidates the distinction between ‘person’ or ‘hypostasis’ and ‘nature’ or ‘essence’. While the terminology he was using was perhaps somewhat new, the conceptual difference between the person, or the individual, and nature, or essence, which is common to many individuals, is a very old one, logically necessary to articulate a Nicene version of the doctrine of the Trinity. The idea of this distinction is important for sake of understanding the development of trinitarian doctrine over time. The entire letter can be read here: https://www.ccel.org/ccel/schaff/npnf208.ix.xxxix.html.
“1. Many persons, in their study of the sacred dogmas, failing to distinguish between what is common in the essence or substance, and the meaning of the hypostases, arrive at the same notions, and think that it makes no difference whether οὐσία or hypostasis be spoken of. The result is that some of those who accept statements on these subjects without any enquiry, are pleased to speak of “one hypostasis,” just as they do of one “essence” or “substance;” while on the other hand those who accept three hypostases are under the idea that they are bound in accordance with this confession, to assert also, by numerical analogy, three essences or substances. Under these circumstances, lest you fall into similar error, I have composed a short treatise for you by way of memorandum. The meaning of the words, to put it shortly, is as follows:
2. Of all nouns the sense of some, which are predicated of subjects plural and numerically various, is more general; as for instance man. When we so say, we employ the noun to indicate the common nature, and do not confine our meaning to any one man in particular who is known by that name. Peter, for instance is no more man, than Andrew, John, or James. The predicate therefore being common, and extending to all the individuals ranked under the same name, requires some note of distinction whereby we may understand not man in general, but Peter or John in particular.
Of some nouns on the other hand the denotation is more limited; and by the aid of the limitation we have before our minds not the common nature, but a limitation of anything, having, so far as the peculiarity extends, nothing in common with what is of the same kind; as for instance, Paul or Timothy. For, in a word, of this kind there is no extension to what is common in the nature; there is a separation of certain circumscribed conceptions from the general idea, and expression of them by means of their names. Suppose then that two or more are set together, as, for instance, Paul, Silvanus, and Timothy, and that an enquiry is made into the essence or substance of humanity; no one will give one definition of essence or substance in the case of Paul, a second in that of Silvanus, and a third in that of Timothy; but the same words which have been employed in setting forth the essence or substance of Paul will apply to the others also. Those who are described by the same definition of essence or substance are of the same essence or substance when the enquirer has learned what is common, and turns his attention to the differentiating properties whereby one is distinguished from another, the definition by which each is known will no longer tally in all particulars with the definition of another, even though in some points it be found to agree.
3. My statement, then, is this. That which is spoken of in a special and peculiar manner is indicated by the name of the hypostasis. Suppose we say “a man.” The indefinite meaning of the word strikes a certain vague sense upon the ears. The nature is indicated, but what subsists and is specially and peculiarly indicated by the name is not made plain. Suppose we say “Paul.” We set forth, by what is indicated by the name, the nature subsisting.”
Its noteworthy then that Basil understood ‘essence’ as a generic nature shared by multiple distinct persons. When the Son was confessed to be ‘co-essential’, that is, of the same essence as the Father, then, what was being communicated was the idea that Christ shared a common nature or genus with His Father. Over the following centuries, that view would be replaced by the alternative view that the one essence that the Father and Son share is a person, who is them both; the heresy of semi-modalism.