Derived from the Latin word filius (meaning 'a son'; cf. 'filial piety'), filiation is the noun used by theologians to describe the state of Christ as "the eternally begotten Son" of God (as, e.g., "filiation belongs to the Son, while procession is ascribed to the Holy Spirit").
Filioque (pronounced fi-li-o-kuay) refers to the phrase "and the Son" found in the Latin text of the Nicene Creed as in:
I believe in the Holy Ghost, the Lord, the Giver of life who proceeds from the Father and the Son . . .
The question of the relationship between the three "persons" of the Trinity has had a long history, beginning with the first attempt to formulate a clear definition of it in the Nicene Creed of 325 and 381. Sometime in the late 5th-early 6th Cent, however, a number of Latin (Western) churches thought they could clarity the relationship more distinctly by adding—independently and without warrant of any council—the filioque to the text of the Creed, which Rome formally incorporated into its confession of faith in 1014. The addition (which, of course, also raises questions of how we are to understand it) impinges significantly on how we understand the nature of the Trinity. The Eastern Greek-speaking churches objected strenuously to it, and the seed of division was sowed which would eventually lead to the formal break between the Eastern Orthodox Church and Rome in 1054 (nowadays referred to as the Great Schism). Though hidden from public view most of the time, the filioque continues to raise questions among Christian theologians.
Resources:
Gerald Bray, "Filioque and Anglican-Orthodox Dialogue," Churchman 93.2 (1979): 123-134.
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Gerald Bray, "The Filioque Clause in History and Theology," Tyndale Bulletin 34 (1983): 91-144.
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Nick Needham, "The Filioque Clause: East or West?" Scottish Bulletin of Evangelical Theology 15.2 (Autumn 1997): 142-162.
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Jake Eggertsen, "Is the Filioque Clause Biblical? Foundations 77 (Autumn 2019): 30-44.
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