The clearest line The Book of Coming Forth by Night draws is theological, and it is drawn against the very organization Aquino had just left. Anton LaVey's Satanic Bible is explicit that Satan is a symbol, a name for carnal instinct and self-interest, not a being anyone actually prays to. Aquino's text reverses that claim entirely.
Set, in the book's own account, is not a metaphor for anything. He is presented as a genuinely existing, self-aware entity, the original of the figure later traditions folded into Satan, and the Temple of Set exists to recognize and engage with that being directly rather than to use his name as a rhetorical device. This is why Aquino insisted the Temple was a departure from Satanism rather than a variation on it: LaVeyan Satanism is built on atheism performed through religious imagery, and the Temple's founding text rejects that atheism outright in its very first pages.
The book frames the shift in explicitly ambitious terms, describing the founding of the Temple as opening a new phase it calls the Aeon of Set, succeeding the Aeon of Satan the Church of Satan had claimed to open nine years earlier. Whatever else divides the two organizations, that theological line, symbol against real being, is the one the founding text itself draws first and treats as the whole reason for existing separately at all.