What's the difference between i.e. and e.g.?
early 13c., "the Father, Son and Holy Spirit," constituting one God in prevailing Christian doctrine, from Old French trinite (11c.), from Latin trinitatem (nominative trinitas) "Trinity, triad" (Tertullian), from trinus "threefold, triple," from plural of trini "three at a time, threefold," related to tres (neuter tria) "three." The Latin word was widely borrowed in European languages with the rise of Christianity (e.g. Irish trionnoid, Welsh trindod, German trinität).
a word not found in Scripture, but used to express the doctrine of the unity of God as subsisting in three distinct Persons. This word is derived from the Gr. trias, first used by Theophilus (A.D. 168-183), or from the Lat. trinitas, first used by Tertullian (A.D. 220), to express this doctrine. The propositions involved in the doctrine are these: 1. That God is one, and that there is but one God (Deut. 6:4; 1 Kings 8:60; Isa. 44:6; Mark 12:29, 32; John 10:30). 2. That the Father is a distinct divine Person (hypostasis, subsistentia, persona, suppositum intellectuale), distinct from the Son and the Holy Spirit. 3. That Jesus Christ was truly God, and yet was a Person distinct from the Father and the Holy Spirit. 4. That the Holy Spirit is also a distinct divine Person.