Two traditions about the meaning of Hypostasis

From the book The Person in the Orthodox Tradition by Metropolitan of Nafpaktos Hierotheos, and translated by Esther Williams

""The term 'hypostasis' has two meanings. Sometimes it means simple existence. In this sense the hypostasis is connected with the essence, and this is why certain of the Fathers have said: "the natures, that is to say, hypostasis". At other times it means "the existence of an individual substance in itself", and it signifies the difference of one individual from the other.

It must be pointed out here that these two meanings are given by St. John of Damascus because in the early Church there were two traditions about the meaning of hypostasis. Alexandrian theology associated the essence with the hypostasis, while Cappadocian theology associated the hypostasis with the person. Thus we see that in the Creed as formulated by the First Ecumenical Council the word hypostasis was used in the sense of essence, while finally in the Second Ecumenical Council the teaching was given that the hypostasis is connected with the person and is distinct from the meaning of essence. We see this position also in the Cappadocian Fathers, but we must point out that it was accepted by Athanasius the Great as well. It is a fact that we have no change in theology, but only in terminology. Finally it prevailed that essence is to be associated with nature and hypostasis with person. In any case, essence cannot subsist by itself, since formless essence does not subsist, while in the hypostasis, or individuals, are found both the essence and the intrinsic differences.""

Pages 73-74 The Person in the Orthodox Tradition by Metropolitan of Nafpaktos Hierotheos, and translated by Esther Williams