In their discussion of the Trinity, theologians have developed a number of terms to help explain, as precisely as possible, what God is like. When someone speaks of the “ontological Trinity,” also known as the “immanent Trinity,” it is in reference to the nature of God.
Ontology is the philosophical study of the nature of being. The “ontological Trinity” refers to the being or nature of each member of the Trinity. In nature, essence, and attributes, each Person of the Trinity is equal. The Father, Son, and Holy Spirit share the same divine nature and thus comprise an ontological Trinity. The teaching of the ontological Trinity says that all three Persons of the Godhead are equal in power, glory, wisdom, etc.
The ontological Trinity is also sometimes called the “essential Trinity.” It is often mentioned in conjunction with the economic Trinity, a term that focuses on the relationships within the Trinity and each Person’s role in creation and salvation. The term ontological Trinity focuses on who God is; the term economic Trinity focuses on what God does.
The ontological Trinity is basic Christian doctrine and is foundational to all Christian belief. John 10:30 says that Jesus and the Father are one, by which it is meant that they are of one nature. In Matthew 28:19 Jesus tells us to baptize “in the name of the Father and of the Son and of the Holy Spirit,” clearly equating the three Persons of the Godhead.
Below is the best symbol for the Trinity we are aware of (click to expand):