Democrat House Intelligence Committee chairman Silvestre Reyes was embarrassed recently for not knowing the difference between the Sunni and Shiite (aka Shia) Mohammedans, so I looked it up.
Before Mohammed died in 632 AD, he tried to pass control of his kingdom to Ali, his cousin who had also married his daughter and had a couple of sons with her. He also had many other wives. The Shiites believed that Ali had the right genes for talking to God, and the Sunnis believed that power should be shared with other high priests (aka imams). So they fought a war over it, and both sides have been mad about it ever since.
There isn't much practical difference between the Sunnis and Shiites, except that the Sunnis put their foreheads on a prayer mat while praying, and the Shiites put the foreheads on a hard block of clay. Also, they regard each other as heretics who should be persecuted or killed like other infidels.
Most Mohammedans are Sunnis, including Saudis, Al-Qaeda, and Saddam Hussein. Shiite influence is on the increase, because of Iranian influence, the introduction of democracy in Iraq, and the success of Hezbollah in Lebanon.
I tried to figure out which faction is better, but I gave up. Trying was a bit like distinguishing Nazis and Commies. They are all dedicated to the destruction of much of what the civilized world consider great.
Update: Here is the NY Times version. It also describes additional splits. Most of the Shiites are "twelvers", meaning that they are still upset that the boy who was supposed to become the 12th imam disappeared in 874 AD.