Homoiousios (Greek: ὁμοιούσιος from ὅμοιος, hómoios, "similar" and οὐσία, ousía, "essence, being") is a Christian theological term, coined in the 4th century to identify a distinct group of Christian theologians who held the belief that God the Son was of a similar, but not identical, essence (or substance) with God the Father.
[1][2] During the period of the development of Christian doctrine and refinement of Christian theological language which ran from AD 360 to 380, the controversy between Arianism and what would eventually come to be defined as catholic orthodoxy provoked an enormous burgeoning of new movements, sects and doctrines which came into existence in the attempt to stabilize and consolidate a unique and universal position on complex and subtle theological questions.
One of the central questions concerned the nature of God and the fundamental character of his relationship with his Son Jesus Christ as the preexistent Logos.
Hanson refers to this as "Neo-Arianism" and as “a new and radical theology” that appears for the first time in the extant ancient records in the form of the “Second Creed of Sirmium of 357,” afterward approved by a larger synod at Antioch (probably in AD 358).
For example:“Anathema 13 links the error of thinking of the Father/Son relationship in corporeal terms with that of making the Son identical with the Father.”[9]: 356 Homo-i-ousianism did not accept this notion.
Basil explained: Anathema 13 “damns him who declares ... that the Son is identical with the Father … This is manifestly directed against N (the Nicene Creed).”[9]: 355
For that reason, in this view, "the Son is 'unlike' (anhomoios) in ousia to the Father” Ayres refers to this as "Heterousian (different substance) theology."
At a council in 358 at Sirmium, at the height of the movement's influence, the claim was made that the Son is "like [the Father] in all [respects]" (ὅμοιον κατὰ πάντα, hómoion katà pánta), while the use of οὐσία (ousía) or any of its compounds in theological discussion was strongly criticized but not abandoned, and the heteroousians were anathematized.
… … Thus, although Basil of Ancyra was influential with the imperial authorities at one point during 358–9, it was not for long, and he never seems fully to have overcome long-standing Homoian influence at court.
The result was that the Homoiousians disappeared from the stage of history and the struggle to define Church dogma became a two-sided battle between the Homoousians and the Homoians.
We may even think of Basil's major dogmatic work, the Contra Eunomium, as the logical conclusion of one strand of Homoiousian theology.”[4]: 189 “Around 360,” “Basil lets us know his preference for the phrase (‘invariably like according to essence’) to describe the relationship of Father and Son.” This is similar to the standard Homoiousian phrase “similar substance.” He has a “preference for Homoiousian-sounding language.”[4]: 189