As far as I am aware, while they tried to distance themselves, they are the same or closely aligned and/or worked together. Lon Milo Duquette and Manly Palmer Hall have shed a little light on the affiliations, and so called Egypt and Babylon, etc. (Mozart's Magic Flute being a particularly delightful backstory).
It's also interesting that so many worshipped in churches while also bringing to AA, OTO, Golden Dawn, which I'm not particularly adverse to, since I've learned to properly understand religions as esoteric rather than exoteric, and I'm not even against Masons or illuminati, per se, but a lot of these people got lost in the sauce and let power go to their heads.
https://www.britannica.com/topic/Bavarian-illuminati
That said, Freemasonry probably has farther reach. I can't really provide more links, since this work was just a personal interest that I looked into for a few decades and didn't really keep a running file.