This misinterpretation comes from Christians, actually.
Historically, Christians' aversion to other faiths has compelled them to lump wide, disparaging opinions into one blanket term, such as "paganism" or "heathenism." A "pagan" or a "heathen" is simply one who does not subscribe to the three major world religions - Christianity, Islam and Judaism.
In the same spirit, modern Christians have associated everything from Wicca to Harry Potter as "the Devil's work," hence the misnomer.
The truth is, "Satanism" is itself a blanket term to describe any religion that worships Satan. Satan as a religious icon has taken many forms throughout history, and the various sects that revere him reflect this fact. There is Luciferianism, a form of Satanism that worships Lucifer as a guardian angel and patron deity of truth. There's Biblical Satanism, the kind most people think of when they hear the term 'Satanism;' Biblical Satanists revere the Judeo-Christian interpretation of Satan as an evil dark lord. Then there's LaVeyan Satanism, a form of atheistic self-worship espoused by Anton LaVey, the 'Black Pope,' and the Church of Satan, established in California on April 31st, 1966.
The Illuminati is a fictional Enlightenment-era secret society, and the subject of many conspiracy theories.
I hope that helps.