I should clarify that when Cindy is talking about how “Unitarians” are universalists, she means the UUA, the stereotypically pluralist group. They are quite different from unitarian Christians per se (though the group somehow morphed from Christian groups both unitarian and universalist), and their universalism is more pantheistic or just vaguely feel-good positive than what Christian universalists typically believe.
Unitarian Christians might or might not be universalists; just like they might or might not be Calv or Arm equivalents. But there aren’t many unitarian Christian groups and the UUA kind of farms noteriety 
, so just like the UUAs give Christian universalists a bad image they give Christian unitarians a bad image, too.
As for Dave’s multiple trinitarian type list… 
Different kinds of modalism (whether naturalistic or supernaturalistic theism) where God manifests in three ways but not in three distinct persons, are not the Trinity. Polytheisms with three lesser lords or gods, are not the Trinity. Cosmological Tri-theisms where there are three distinct independent facts of reality, are not the Trinity. They are not different varieties of the idea of one and only one ground of all reality being three distinct persons relating personally to one another. Nor are different technical disputes about how the persons of the Trinity inter-relate to one another, multiple different trinitarian theologies.
Regaring monotheists being non-Trinitarians: many monotheists are not trinitarian (unitarian and modalist Christians aren’t, non-Christian Jews aren’t, Muslims aren’t, binitarian Christians aren’t – I’ve only ever read one of those, who also happened to be a universalist incidentally to his binitarianism), but trinitarians are also monotheists – one and only one God Most High is the foundation and source of all reality. That isn’t tri-theism or bi-theism (three or two ultimate foundations of all reality), and it isn’t polytheism (x-number of lesser gods dependent upon an overarching foundational reality). Whether someone judges that the Trinity collapses logically into something that ultimately isn’t trinitarian theology, is irrelevant for distinguishing conceptual categories: I think cosmological tri-theism logically collapses into polytheism, but I recognize and understand the conceptual distinction of what cosmological tri-theists (some Mormons primarily) are trying to claim.
Modalists, who are non-trinitarians (and even anti-trinitarian), affirm the Holy Spirit is the one and only God Most High just like the Father and the Son. They deny that the Holy Spirit is a distinct person personally interacting with the Father or the Son (and deny that the Father and the Son are actually interacting with one another, these just being modes of God’s operation and nothing more.)
Some unitarian Christians (there being historically many subvarieties) also affirm the Holy Spirit is God Most High, not a creature like the Son. But they consider the HS only a mode of God, another name for the Father. (Theoretically a unitarian Christian could regard the Son as only a mode of God’s operation, another way of naming or describing the Father, while believing the Spirit to be a not-God creature or lesser god produced by God. I don’t recall ever reading about such Christians, but technically it’s a unitarian option.)
In theory someone could be a bi-theist and regard the Father and the Holy Spirit as two Gods Most High while the Son is a not-God creature produced by one or both of Them. That wouldn’t be monotheism, and so wouldn’t be the same as the HS also being the one and only God Most High along with the Father, but the Spirit and the Father would both be a God of that type on this theology. (Perhaps a Goddess Mother Most High, per the frequent feminine grammar in Judeo-Christian scriptures, with the Son being Their first creation or a creature They adopted as their leading son or something like that.)
A cosmological tri-theist could consider the third God Most High to be the Holy Spirit of Christian theology. (A tri-theist doesn’t have to be a variety of Christian of course; something like Zeus, Gaia, and Hades, could be the three independent ultimate grounds of all existence.) Theoretically I suppose someone might go for four or more Gods Most High borrowing Judeo-Christian data, with the Holy Spirit being one of those.
Finally (?), someone could be a… hm, what to coin the term… a quartitarian Christian theist? One and only one God Most High but four Persons relating to one another not only three. Bulgakov, the great Russian Orthodox systematic theologian, comes close to this, although he explicitly avoids making the position, in how he treats the deity of the Trinity as a personal impersonal power or something like that which the Three Persons interact with distinctly. (I’m not a big fan of this move. ) But someone could go with Wisdom, perhaps, as the Fourth Person.
This does have some relation to Dave’s (otherwise somewhat facetious) list of multiple trinitarian Christianities: none of those options would be a different Trinity, but there are a lot of complexities involved in distinguishing types of theological options. Orthodox trinitarian Christian theism may be hard to believe, and isn’t hard to specify (despite some subtle sub-variations, like whether the Spirit proceeds from both the Son and the Father or only from the Father alone), but it isn’t simply the same as “Jesus being God” or even “Jesus and the Holy Spirit being God”.
And now you have something more for your OD-C to OCD about. 
) of the people even on this Forum would show that they are unaware of the number of theories out there, and if they did become aware of them, might be a little more circumspect about calling any particular theory ‘essential’ to being a Christian or, worse, calling those who disagree -deniers of the faith.
