Following are definitions of Christian ideas of the Godhead, based on their respective articles at Wikipedia.com.
Arianism is the belief that Jesus was not one with the father, and that he was not fully (although almost) divine in nature, as taught by Arius (c. AD 250-336). Arius lived in Alexandria, Egypt in the early 4th century.
Binitarianism is the belief of two in one God, as opposed to one (unitarianism) or three (trinitarianism).
Nontrinitarianism includes all Christian belief systems that reject the doctrine of the Trinity -- that the God of the Bible is three distinct persons in one being.
Sabellianism (also known as modalism, modalistic monarchianism, or modal monarchism) is the belief that the Father, Son and Holy Spirit are different modes or aspects of one God, as perceived by the believer, rather than three distinct persons.
Trinitarianism is the belief that the one God exists in three Persons and one substance, Father, Son, and Holy Spirit.
Unitarianism is the belief in the single person of God, in contrast to the doctrine of the Trinity.
"Isms-ism" -- there are all kinds of variations that spin off of these beliefs.