Freemasonry started before the illuminati, those who started the illuminati, basically bit off freemasonry
Those who started the Illuminati were Freemasons, with their brand of "Illuminated Freemasonry", still holding credence today amongst the "adepts" in the high degrees.
Adam Weishaupt and Freidrich von Knigge were members of the Lodge of Munich, with Weishaupt incorporating ideas learned from Masonry and his days as a Jesuit into the logic of the Illuminati.
Illuminati stands for enlightened ones, but most importantly means "Illuminated Freemasonry."
Funny how they met the same "demise" into the underground as the Knights Templars did, into high-degree Freemasonry.