Today, biblical Unitarianism (or "Biblical Unitarianism" or "biblical unitarianism") identifies the Christian belief that the Bible teaches God is a singular person—the Father—and that Jesus is a distinct being, his son. A few denominations use this term to describe themselves, clarifying the distinction between them and those churches which, from the late 19th century, evolved into modern British Unitarianism and, primarily in the United States, Unitarian Universalism.
The history of Unitarianism was as a "scripturally oriented movement" which denied the Trinity and held various understandings of Jesus. Over time, however—specifically, in the mid-19th century—Unitarianism moved away from a belief in the necessity of the Bible as the source of religious truth. The nomenclature "biblical" in "biblical Unitarianism" is to identify the group/s as not having made such a move.
The term "biblical Unitarianism" is connected first with Robert Spears and Samuel Sharpe of the Christian Life magazine in the 1880s. It is a neologism that gained increasing currency in non-Trinitarian literature during the 20th century as the mainstream Unitarian churches moved away from belief in the Bible and, in the United States, towards merger with Universalism. It has been used since the late 19th century by conservative Christian Unitarians, and sometimes by historians, to refer to Scripture-fundamentalist Unitarians of the 16th-18th centuries. Its use is problematic in that Unitarians from the 17th century until the 20th century all had attachment to the Bible, but in differing ways.
Read more about Biblical Unitarianism: Early Unitarians and The Bible, The Unitarian Churches (1774 Onwards), First Uses of The Term, Modern Use of The Term, Denominations