According to the Weekly Standard
Al Qaeda In Iraq is part of the global al Qaeda movement. AQI, as the U.S. military calls it, is around 90 percent Iraqi. Foreign fighters, however, predominate in the leadership and among the suicide bombers, of whom they comprise up to 90 percent, U.S. commanders say. The leader of AQI is Abu Ayyub al-Masri, an Egyptian. His predecessor, Abu Musab al Zarqawi, was a Jordanian.
The group is a direct successor of al-Zarqawi's previous organization, Jama'at al-Tawhid wal-Jihad. Beginning with its official statement declaring allegiance to the Osama bin Laden's al-Qaeda terrorist network in October 2004, the group identifies itself as Tanzim Qaidat Al-Jihad fi Bilad al-Rafidayn (QJBR) ("Organization of Jihad's Base in the Country of the Two Rivers").
OK. So Al Qaeda in Iraq is a part of Al Qaeda, ideologically and structurally. Whether they have all the resources of the greater Al Qaeda body or not is unclear, but that they will fight for Al Qaeda proper's aims is not. Nobody complains when someone calls prostate cancer 'cancer' because prostate cancer is relatively treatable, as if they were trying to exaggerate the seriousness of the situation.