To answer today’s question: when the UUA position of Moderator was created in 1961, it was a much more substantial position than it is today. Originally this person was in charge of financial responsibility in the Association. The Moderator, along with the Board, was supposed to be in charge of creating the actual policies of the UUA. And at the same time, the President had considerably less powers, and was expected to carry out those policies, not make them. But conflicts, including simple personality clashes between the President and Moderator, led to the Moderator being demoted and the President being given more power than originally intended (yet, these power struggles/personality conflicts also reduced the term limits for the President from twelve to only eight years).
Today the Moderator is basically just the Officer of the Board who presides at meetings, as well as moderates at General Assembly. Unlike the President it is an unpaid position and has evolved into one typically filled by laywomen, as opposed to the President, which has been a paid position typically filled by male ministers.
By the way, here’s a little extra trivia for today: William Howard Taft was the Moderator of the AUA after he served his term as President of the United States.