Here’s a later (partisan, 20th century Unitarian) account of one of several trinitarian controversies in early modern England, started by men within the Church of England who would have considered themselves Christians and trinitarians, but who rejected mainstream medieval trinitarian thinking, especially as embodied in the “Athanasian” creed. During this controversy, these dissenters started using the term “Unitarian”, as they disliked being tarred as “Socinians“, which most of them were not. In this period, “Unitarian” just means something like “anti-Athanasian” – it would include modalists, various kinds of subordinationists (Arian and otherwise), creedal minimalists, as well as some who held “humanitarian” views about Christ (i.e. holding that he was only a man, who was not divine, and who did not pre-exist his conception in Mary – like later “Unitarians”.)
The Trinitarian Controversy, as this is commonly called, was started in 1687 by the publication of the Brief History of the Unitarians or Socinians [an anonymous tract written by the Reverend Stephen Nye (1648-1719)] …This tract gave an account of the Unitarians and their beliefs from the early Church down, and refuted the proof texts usually quoted by the Trinitarians in support of their doctrine, ending with the conclusion that those holding Unitarian views of the Trinity ought not to be prosecuted for them, but should be received in the Church as brethren. This tract was soon followed by another, Brief Notes on the Creed of St. Athanasius, which took up the Creed clause by clause, laid bare its contradictions with itself, reason, and Scripture, and concluded that it ought not to be retained in any Christian church.
These tracts were widely read and made a great stir among both clergy and laity; and seeing the doctrine of the Trinity thus attacked, one bishop or doctor after another now came forward to defend it. Some maintained, against the charge that the doctrine was unreasonable or self-contradictory, that it ought to be reverently accepted on faith as a sacred mystery, above human comprehension; to which was replied that this was precisely the argument which Roman Catholics had urged in behalf of some of their own most objectionable doctrines, and which Protestants had steadily refused to admit as sound. Some sought to prove that the doctrine was supported by Scripture; but in this they were all too easily confuted by the Unitarian writers. Others, appealing to antiquity, tried to show that this had been the teaching of the Christian Church from the beginning; but the Unitarians, while not unwilling to admit that belief in some sort of Trinity was at least consistent with the Bible, and was supported by the early Fathers of the Church, insisted that it was far from being the kind of Trinity so carefully defined in the Athanasian Creed. The crucial question in the controversy was as to what is meant by one God in three persons. When the Unitarians urged that this belief by its own words contradicts itself, some tried to remove the difficulty by explaining that persons means just what we usually mean by the word; but the Unitarians replied that this involves belief in three separate Gods. Others sought to show that persons has here a special meaning, and simply means three different modes of being or acting; but it was replied that this was the ancient heresy of Sabellianism, and that Christ means something more than merely Godâ€™s mode of acting. So the controversy went on, with the Unitarians ever keen to detect any flaw in the reasoning of the orthodox, and ready to press every advantage against them. The controversy ended, the acute stage of it at least, when the authorities of the Church at least seemed to accept an explanation of the Trinity to which the Unitarians could assent with good conscience. (Earl Morse Wilbur, Our Unitarian Heritage, (1925), 198, emphasis added)
In a later discussion of this same controversy Wilbur is a little clearer about how the controversy ended. I believe he’s adopting Nye’s terminology when he distinguishes between “Real” and “Nominal” trinitarians.
It had never been [Nye’s] purpose to deny the doctrine of the Trinity outright, for he was an active clergyman in the [Anglican] Church, but rather to find recognition within its fold for a definition of the doctrine in terms to which Unitarians like himself could with clear conscience agree. The controversy stirred up by these tracts called forth contributions from a dozen or so of Bishops, clergymen, scholars, and Dissenting ministers. …They differed widely in the explanations that they offered of the doctrine, and at least six distinct ones were proposed, to some of which no very serious objection was felt. The writers fell in the main into two general classes, the Real and, the Nominal Trinitarians. The Real Trinitarians took the Trinity literally in terms that fell little short of bald tritheism, and defended it as ultimately an inexplicable mystery; but this view, when once clearly stated and avowed, was ere long disowned and rebuked by authority as heretical. The Nominal Trinitarians on the other hand met the challenge not by taking the terms of the doctrine in their literal meaning as language is used today, but by going back to what it was maintained had been their ancient sense. Although in the common mind this aroused no suspicion of heresy, it was in fact practically Sabellianism. But since this view had now been favored by several Bishops whose orthodoxy was beyond question, the Unitarians became satisfied that the majority of the Doctors of the Church did not mean by their scholastic terms any sort of tritheism (which was what they had objected to), but only a ‘Nominal’ Trinity, and hence they regarded themselves as sound and orthodox churchmen. Having thus found room for themselves within the Church, they were therefore content to abide in peace, and largely withdrew from the controversy, which now began to drift into other channels, and left the conservatives within the Church to carry on disputes with one another. (Earl Morse Wilbur, A History of Unitarianism: In Transylvania, England and America, Volume II (1952), 133-4, emphasis added)
In a nutshell: these early “Unitarians” were concerned to maintain unequivocal monotheism. When they challenged the mainstream, Athanasian Anglican trinitarians, they were given a modalist reply. Since modalism is a kind of unequivocal monotheism, the Unitarians (for the most part) went away happy!