Ontological trinity (ontology, study of being and essence) "Each of the three persons in the Godhead are divine, have equal attributes (omniscience, omnipresence, holiness, etc.)."
Economic Trinity (economic, from the Greek oikonomikos, which means relating to arrangement of activities)
To be overly simplistic, we could say that the Ontological Trinity deals with what God is and the Economic Trinity deals with what God does.
As economic subordination is easily confused with Arian subordiationism this is a good comprehension about the matter.
How important therefore to find easy definitions. Both explanations are conceptualisations of our thoughts about methaphysical objects,God,holy spirit, Son, what is their nature, essence and in which relation they are.
Onto ="being", "logy"=theory
About concepts of "Ontology" - application of the philosophical concepts about speaking about being and existence and the application in the computational domain.
How Ontologies are used in Information/Knowledge Management: