What do non-trinitarians mean when they call Jesus the "Son of God"? On a different question I got an answer and some comments. One of which said:


  Generally, when a Christian says that Jesus is the "Son of God" they are referring to the doctrine of the Trinity, where Jesus is a person of a three-part godhead. It's a complicated doctrine that necessitates antinomy. As for your friend's reasoning, it is sound, and is the same reason we call Adam, from Genesis, the son of God also, for he also had no human father, instead God fashioned him from the clay of the Earth and breathed life into him. –  fredsbend yesterday 


If that is what Trinitarians usually mean when they call Jesus the "Son of God", what do non-trinitarians mean when they say it?
I've come across a few different meanings. Here are three examples:


Adoptionism: Jesus was born just a man, but was adopted as God's own Son. There are a few reasons that are given for this (simply from God's grace; Jesus was the supreme religious expert for two examples). Those who defend this position often point to Jesus's baptism as the moment that this adoption took place.
Arianism: Jesus is from a divine substance like the Father, but of a different divine substance than the father. Obviously, the parts of the Nicene creed came from this, declaring that Jesus was begotten before all ages.
Unitarianism: Jesus is a religious exemplar, and we should aspire to have the religion of Jesus, not a religion about Jesus.


There are all manner of permutations of these ideas, as can be seen in the article on Wikipedia about Christological heresies.