Incase of correction, the Illuminati does Not branch from the Freemasons. The Illuminati is the higher up branch of the Rosicrucian order.
The freemasons equivalent branch is the Knights Templar, varying from degrees 10 - 15 and up depending on the root of the lodge you are initiated into.
They have similar goals of 'enlightenment' However, the freemasons focus on charity work, while the Rosicrucian order is much more spiritualistic in their rituals. They're also a much smaller organization, with freemasons having lodges from every other town to the rosicrucians being lucky to have one in every state.
I've had relatives and friends in both organizations, their lodges and people are really interesting and worth reading into.