A fraternal organization dating back to the 14th century, traditionally the Freemasons are considered a “fraternity” of sorts for stonemasons. The groups would meet regularly in their Masonic Lodge, and conduct business under several guiding principles, including that members have “a belief in a supreme being,” that only men are allowed, and that — despite lodges being asked to display scripture — there should be no discussion of politics or religion.
However — due, most likely, to the groups use of ceremonial regalia and other archaic rituals — the Freemasons have long been associated, at least in rumor, with the occult. In particular, many religions object to Freemasonry on conspiracies that the organization is involved in mysticism, occultism, and Satanism.
The Freemasons rarely respond to such claims, having stated only that : “Freemasonry is not a religion, nor a substitute for religion. There is no separate ‘Masonic deity,’ and there is no separate proper name for a deity in Freemasonry.” (Source.)
The Bavarian Illuminati is a real-life secret society dating back to the 1700s. Granted, much of what we do know about the Illuminati is questionable — and the group has become the source of many conspiracy theories. According to Wikipedia:
Historically the name refers to the Bavarian Illuminati, an Enlightenment-era secret society founded on May 1, 1776 to oppose superstition, prejudice, religious influence over public life, abuses of state power, and to support women’s education and gender equality. The Illuminati were outlawed along with other secret societies by the Bavarian government leadership with the encouragement of the Roman Catholic Church, and permanently disbanded in 1785. In the several years following, the group was vilified by conservative and religious critics who claimed they had regrouped and were responsible for the French Revolution.
In subsequent use, “Illuminati” refers to various organizations claiming or purported to have unsubstantiated links to the original Bavarian Illuminati or similar secret societies …
You can read more scholarly information about the Illuminati here.