In their snarky exchange about al-Qaida and Iraq, presidential contenders John McCain and Barack Obama have missed an important point – the group called al-Qaida in Iraq is not an offshoot of the larger al-Qaida, which supposedly has been the target of the U.S. war on terrorism for more than six years. Instead, al-Qaida in Iraq is a group of Sunni extremists that only began going by the attention-getting name in 2004 and is only loosely affiliated with the larger terrorist organization headed by Osama bin Laden.

Further, the Iraqi group contacted Osama bin Laden’s al-Qaida, pledging support for its terrorist operation. Al-Qaida did not spin off a branch in Iraq, which is what it appears supporters of the Iraq war want Americans to believe.

Therefore, saying al-Qaida is in Iraq is an oversimplification.

In a debate Tuesday, Sen. Obama was asked about the potential for the U.S. to go back into Iraq to suppress an insurrection after downsizing the U.S. troop presence. “If al-Qaida is forming a base in Iraq, then we will have to act in a way that secures the American homeland and our interests abroad,” the Democratic candidate said.

A day later, Sen. McCain, the presumed Republican nominee, said he had news for Sen. Obama: “Al-Qaida already has a base in Iraq. It’s called al-Qaida in Iraq,” McCain said. Sen. Obama fired back: “I have some news for John McCain, and that is that there was no such thing as al-Qaida in Iraq until George Bush and John McCain decided to invade Iraq.”

Both men are only partially right.

According to the U.S. State Department, al-Qaida in Iraq went by more than a dozen names, including The Organization of al-Jihad’s Base in the Land of the Two Rivers and the Al-Zarqawi Network, after the group’s founder, Abu Musab al-Zarqawi, who was killed in 2006.

The group declared its allegiance to al-Qaida in October 2004, more than a year after the U.S. invasion of Iraq. A year later, Mr. al-Zarqawi outlined plans to expand the war in Iraq by expelling U.S. troops, spreading the fighting to secular neighborhoods and drawing Israel into the battle.

Al-Qaida in Iraq’s efforts to unify Sunni insurgents largely have failed because of its extreme fundamentalist doctrine and its violence against civilians, including kidnappings and beheadings. In fact, more moderate Sunni groups are fighting against al-Qaida in Iraq, as are Shiite fighters.

These important details were lost in the testy exchanges between the candidates but will remain important for whoever moves into the White House next January.