You say Shia and I say Sunni

Let's call the whole thing off. Neatorama explains (via a reprinted article from the mental_floss book "What’s the Difference?" with permission) the difference:

After the prophet’s death on June 8, 632, a gathering of his followers met at Medina and proclaimed Abu Bakr (kinsman, companion, and early convert of Muhammad) caliph, or political leader. The claim stemmed from his close relationship with Muhammad, and the fact that Muhammad had asked Abu Bakr to lead prayers when too ill to do so himself. Those who recognize Abu Bakr and his three immediate successors, called the Four Rightly Guided Caliphs, are referred to as Sunni Muslims, and today almost 90 percent of Muslims worldwide fall into this category.

One group of followers, however, refused to accept Abu Bakr. These Rafidi ("Refusers") supported the claim of Ali ibn Abi Talib, Muhammad’s cousin (and son-in-law). The claim is based on a sermon the Prophet had given at Ghadir Khum, in which Muhammad referred to Ali as mawla, which some translate as "master." Ali’s supporter called themselves Shiat Ali (the Party of Ali), though today they are known as simply Shia. Ali did eventually ascend as the fourth caliph. To Sunni, he is the last of the Four Rightly Guided Caliphs. But to Shias, he is the first caliph and, more important, the first Imam - a word Shia Muslims use to refer to the person chosen leader of all the faithful.

While they and the Sunnis both revere the Koran, they accept different hadiths (oral traditions), so their laws are different. Many Shias, for example, allow temporary marriage. Shias also recognize esteemed imams as supreme expert on Islamic law, called Ayatollahs or, for the really big guys, Grand Ayatollahs. As for the locations where Shias have a significant Muslim majority, there are really only two: Iraq and Iran.

Much is made of the differences between Shias and Sunnis, but almost all the violence between them in the past 50 years has been caused, directly or indirectly, by Saddam Hussein - a nominal Sunni who by his own admission was never religious.

Update: Fixed link.