The classic orthodox doctrine of the trinity- as explained in the Eerdman’s Dictionary–
In the early third century Tertullian introduced the expression “three persons, one essence,” meaning by “persons” (Lat. personae) “faces” or “masks.”
But this was soon distorted-
Later in that century Sabellius developed from Tertullian’s rather imprecise terminology the alternative doctrine of modalism (also called Patripassianism [lit. “the Father suffers”] or Theopascism [“God suffers”]). According to Sabellius, Father, Son, and Spirit are three transitory modes in which God manifests himself (cf. the popular analogy of the three persons to water, ice, and steam), not three distinct entities in the Godhead.
(This means, by the way, that the Lutheran and Catholic explanation of the Eucharist is modalistic.)
In the fourth century the three Cappadocian Fathers Gregory of Nyssa, Gregory of Nazianzus, and Basil of Caesarea experimented with Tertullian’s schema, substituting the Greek term hypóstasis: “three substances, one essence,” implying three individual existences sharing one essence.
This is the normal view of Orthodox Christianity. God is three existents of one essence. There really are three (and they don’t just seem to be three or appear from time to time in different manifestations as suits the moment) who really are one. It’s a mystery that can’t be grasped by finite minds but the ability to grasp truth isn’t the final arbiter of reality.
In the eleventh century the nominalist Roscellinus took a tritheist position, arguing that to speak in this way of a divine essence shared by three distinct individuals was in fact to speak of three (incarnate) Gods, just as Peter, James, and John as three individual existences who share one human nature are three different persons (cf. the popular analogy of Father, Son, and Spirit as three bulbs emitting the same light).
But of course tri-theism isn’t monotheism, so Roscellinus was rejected and his view declared heresy.
Again in the fourth century Augustine of Hippo sought to explain the trinity in terms of relations within a person or between persons. He pictured the trinity as analogous to memory, intellect, and will within a single mind, and to the triad of the lover, the beloved, and their love.
Augustine was closer – in this instance – to the truth than his descendants. Oddly, modalism is still widely held by Christians even though they don’t know what it’s called or why it’s inaccurate.
So if you believe God the Father died on the Cross, or that the Holy Spirit is Jesus or that Jesus is the Father, you’re a modalist- a heretic.