What's the difference between a Unitarian and a United Methodist Church service?
I don't know the difference between the services, but the Unitarians deny the doctrine of the Trinity -- an ancient Arian heresy. The nature of the argument deals with same substance (homo ousion: Trinitarians) vs. like substance (homoi ousion: Arians).
Trinitarians hold that the Son of God, though a distinct person, is of the same nature, essence, and being of the Father -- eternally begotten (not created). Arians believed that the Father created the Son, and that the Son is subordinate to the Father.
This controversy is what brought the Council of Nicea together in 325 A.D. -- this brought about the Nicene Creed, which reflects the basic beliefs of Catholicism, Protestantism, and Eastern Orthodoxy. Homo ousion (same substance) prevailed.