Unity is based in Kansas City and started by the Fillmores, I believe. They are sort of an offshoot of Christian Science/ Power of Positive Thinking/ New Thought that believe in spiritual healing etc.
Unitarianism is a liberal denomination that doesn’t believe in the Trinity or that Christianity is the only true faith. I attended a Unitarian Church for a while and it is kind of an anything goes type place. You will find pagans, atheists, ex-Christians, nominal Christians, Wiccan etc.