As this book review of The Family: The Secret Fundamentalism at the Heart of American Power
points out, it is "... not to be confused with the "flirty fishing" cult known as The Family."
It may be different, but it is also similarly dangerous. The Family(COG) thinks it will exert political control during the millennium (not that that particular doctrine is as dangerous as their others since it won't come to pass), whereas this Family tries to exert political control now, which is definitely dangerous for the world.