Trinitarians are your traditional “god the father, god the son, god the holy spirit” believers. However, there was a doctrine that was just as prevalent in the 17th and 18th centuries; furthermore, there are still adherents of this doctrine — some of whom are reluctant to share their doctrinal convictions due to fears of being labeled blasphemous and/or heretical.
The term “unitarian” was popularized in late 1680’s England as a less pejorative and more descriptive term for those who held God to be identical to one divine person, the Father. It has since been used as a denominational label for several distinct groups, but it is here primarily used in the descriptive, generic sense just stated. (The capitalized “Unitarian” is occasionally used here in the denominational sense.) All these groups have been labeled “antitrinitarian”. Although unitarians are by definition against the pro-Nicene and “Latin” traditions, and many have proudly flown the antitrinitarian banner, others strenuously argued that they expounded the correct trinitarian doctrine, the difference being that the former were promoting rival denominations, while the latter sought to be included in mainstream groups (i.e., traditionally trinitarian churches, or ones which were often assumed to be).
Dating back at least to John Newman’s (1801–90) critique of Arius, a popular narrative among mainstream trinitarians is that it is mainly “rationalists” who reject mainstream trinitarianism, meaning something like: people who refuse to believe things they can’t fully understand or can’t explain, even when those things are divinely revealed (Newman 1890, 221; Williams 2001, 2–6). The term “rationalist” implies some sort of epistemic over-confidence or dogmatism, and usually suggests some underlying moral or spiritual defect(s) as well (e.g., Newman 1890, xiii, 18–24, 133–42, 219–30). This narrative received impetus from late 18th and 19th century English and American Unitarianism, which also revised some other Christian doctrines. (See section 4 below.) Further, “philosophical” (non-biblical) objections have at times been emphasized. Various trinitarian claims, especially those in the “Athanasian” creed, have been criticized as inconsistent. And various claims (e.g., that the three enjoy “perichoresis”) have been criticized as unintelligible. The rationalist explanation, though, is inadequate, as unitarians’ views on the Bible, the place of reason, the usefulness of philosophy, the authority of tradition, miracles, and ecclesiology run the gamut— Anabaptists, Anglicans, Catholics, Congregationalists, deists, Presbyterians, and denominational Unitarians appear in their ranks. The kernels of truth here are that most unitarians hold that some elements of some Trinity and Incarnation doctrines are self-contradictory, and they typically reject mysterian theology. (See main entry section 4.)
In any case, they’re both wrong (I don’t feel the need to expound on that here), but just like the longstanding issue of Calvinism vs. Arminianism, Trinitarianism vs. Unitarianism has persisted for just as long!