ISIS was formerly Zarqawi’s group Jama’at al-Tawhid wal-Jihad a/k/a “Unity and Jihad” or al Tawhid - one of the plots Zarqawi’s mostly Palestinian group was noted for even before the US invasion of Iraq in early 2003 was the 1999 Millennium plot, a plot to simultaneously bomb the international airport in Los Angeles and targets in Jordan, including a popular hotel.
Another was their successful assassination of USAID’s Laurence Foley in Jordan in 2002 by his northern Iraq cell. They also were being used by Saddam to assassinate Kurdish leaders before 9/11 in an apparent effort to eliminate Kurds who would work with any US invasion force, much as one of al Qaeda’s European cells assassinated Afghan leader Ahmed Massood on Sept 9, 2001 to deny us an ally for our counterattack.
Zarqawi’s Baghdad cell in 2002 was happily settled in Sadam’s capital and for reasons I don’t know they murdered a Chaldean nun there by beheading her. This was before ANO leader Abu Nidal’s death in Baghdad, where he allegedly “shot himself in the head” several times.
But Zarqawis group merged with Mullah Krekar's group and Krekar's group did have ranking members who were known to be Iraqi intelligence. Krekar's group also had at least one European cell, a cell in Italy that funneled recruits from Europe through Syria and into Iraq.
Even though Zarqawi ran a training camp that shared personnel with an al Qaeda training camp in the same vicinity in Afghanistan, Zarqawi had not openly sworn an oath of obedience to bin Laden. This "technicality" was glommed onto by the antiwar Democrats and press to insist that these terrorist cells in Iraq were not al Qaeda because he hadn't sworn the oath [as far as our intel knew] and were therefore not at fault for 9/11 and should be off limits to US retaliation for 9/11.
Zarqawi did eventually swear the oath to bin Laden, formalizing his group as a member of al Qaeda. His group also merged with Iraqi general al Dhouri's group of Baathist officials and intelligence personnel and became al Qaeda-in-Iraq. After Saddam's death al Dhouri swore the loyalty oath to Zarqawi before Zarqawi was killed by the US.
Al Qaeda in Iraq [AQII] later became ISIS, then ISIL.