Fair! I tend to think of modern Christian Unitarianism as a creature mostly of central and Eastern Europe, but a very brief bit of research shows how wrong I am. It doesn't help that Canada's equivalent to the UUA is the Canadian Unitarian Council. And that's not touching on the fact that a portion of any UU congregation's membership would self-describe as Christian (as opposed to Unitarian Pagans, or Unitarian Atheists, etc.).

Just to muddy the waters further still, there is (or at least was) also Universalism as a Christian sect! Core message: Christ died to redeem all humankind (universal salvation), so stop worrying about saving your soul or anyone else's, and get on with following his actual teachings.

On another note, the International Council of Unitarians and Universalists, to which both the UUA and the CUC belong, admits explicitly-Christian member organisations. (As does the UK's national equivalent, going so far as to include "Christian" in its full name.)

Religion! It's generally a mess, but Unitarian-Universalism is extra muddy.