Illuminati is a name used by many societies in history and modern times. These groups may be real, or just imaginary, some are confirmed, and some are just rumors. In any case, the General Illuminati refers to the Bavarian Illuminati, which is the least secret of all secret societies in the world. Most "Illuminati" who claim to exist or imagine to exist are usually described as the ancient Bavarian Illuminati in the modern world.
The Latin word for Illuminati literally means "one who is specially inspired". Naturally, there are many unrelated groups in history who call themselves Illuminati. Usually, they claim to have Gnostic scriptures or other similar mysterious information.