Strip away the historical detail and the three Manifestos share a single organizing claim: the universe requires no creator to explain it, and human beings are natural beings within that universe rather than souls temporarily housed inside it. The 1933 document stated this directly, describing the cosmos as self existing and treating the traditional theistic account of creation as an idea organized humanism had simply moved past, a position considerably starker than most American religious statements of its era were prepared to make in public.
That naturalism carries a practical consequence the documents return to repeatedly: since no external authority hands down moral law, human beings have to work out ethics for themselves, using reason and accumulated experience rather than revelation. The later Manifestos extend that reasoning into specific commitments the earlier document never mentioned, human rights, environmental responsibility, and, in the 2003 version, an explicit embrace of scientific method as the most reliable tool available for understanding both the natural world and appropriate human conduct within it.
What stays constant across all three is the refusal to locate moral authority anywhere outside human reason and experience. Where a traditional religious statement of faith points upward to revealed authority, the Manifestos point inward and across, to what people can work out together using the only faculties the documents recognize as available, which is why the association treats all three as a single continuous declaration rather than three unrelated statements.