If you want to understand what the real Illuminati order was about, read either Abbe Barruel's Illustrated History of Jacobinism (1799), or John Robison's Proofs Of A Conspiracy (1798). Both are period works from the era of the French Revolution and the discovery of the Bavarian Illuminati. Both works outline the order's goals, operations, structure, and secret initiations. Per the exposed documents of the order, they existing as the top initiate order within continental Masonry, meaning continental Masonry's higher initiate degrees were Illuminati degrees. John Robison himself was a British Mason, and he wrote Proofs Of A Conspiracy to warn others about the Illuminati order and the many degrees the Illuminati added to Masonry on the continent. Per Robison, Masonry originates from Britain, and has only 3 degrees. But the Masonic lodges on the continent of Europe vial Illuminati influence added more degrees in Europe's lodges, and thus the term 'Continental Masonry' was different than British Masonry. Continental Masonry would become called "Blue Masonry", and it has all the higher 33rd degrees and such.
Many of the U.S. founders were British Masons, not a part of Continental Masonry (which had the Illuminati influences from
Adam Weishaupt's order.)