It’s a little bit like Protestants and Catholics, as people have pointed out, though not exactly.
The schism between Sunni and Shia came much earlier and involved who Muslims believed was the proper successor to the prophet Muhammad. (iirc, Shia thought it should be one of his cousins, but I’ve completely forgot the details—it’s about as exciting as memorizing lists of European kings.)
After the schism, the two sects evolved in theology. The Shia are more like Catholics in that they place religious authority in a more or less priestly structure, the system of imams. They believe that there were a succession of magic imams (sort of like the magic pope-man) who were chosen by God to lead the Muslims after Muhammad. They also believe that the 13th imam, a small child who appears to have died, is actually “in occultation” (magical hiding) and will return during the end times. In the meantime, a religious hierarchy of ayatollahs leads the Shia sect, notably Ayatollah Kheimeini in Iran.
The Sunni do not have such a strict theocratic hierarchy, so they are more like Protestants. There are four “schools” of Sunni theology, sort of similar to Lutherans/Episcapelians/Presbyterians in Christianity.
One subsect of the Sunni, which is not considered one of the four proper schools, is the Salafi/Wahhabi. They are sort of like fundamentalist Christians. These are the fun fellows who command broad authority in Saudi Arabia, they finance mosques all over the world, and their fundamentalist theology is a cousin to that of al-Qaeda and the Taliban.
The Sufis are also not really part of the Shia/Sunni divide (they might be grouped with Sunni, though). Sufism is a mystical Islamic tradition that focuses on one’s relationship with God rather than with politics so much. I’m not sure there’s a good comparison in Christian tradition.