Iraqi Shiite militia fighters hold the Islamic State flag as they celebrate after breaking the siege of Amerli by Islamic State militants, Sept. 1, 2014. Reuters

The Islamic State group, the militant organization active in Iraq and Syria, has rebranded itself several times since garnering international attention earlier this summer. The name itself, one with many iterations -- ISIS, ISIL, the Islamic State and Daesh -- breeds controversy and confusion, and warrants some elucidation.

Islamic State group leaders would simply like to be known as the Islamic State. Why? Because the name brings to mind the group's recognition of a caliphate, a state led by a supreme religious and political leader known as a caliph.

The name ISIS comes from the group's invasion of Syria. ISIS stands for the "Islamic State in Iraq and Syria," or "Islamic State of Iraq and al-Sham," an archaic Arabic term for the region. By 2013, militants had taken control of a lot of territory in Syria. Its leaders no longer thought of themselves as just a presence in Iraq.

Last week, the French government announced that they would use the Arabic-derived term "Daesh" (or Daech, as often spelled in French) in place of their previous name for the Islamic State group, EIIL, or "Etat Islamique en Irak et au Levant." Daesh is shorthand for the full Arabic name for the Islamic State group, al-Dawla al-Islamiya fi Iraq wa ash-Sham. It is sometimes spelled DAIISH or Da'esh.

U.S. President Barack Obama has continued to call the militants ISIL, or the Islamic State of Iraq and the Levant. The Levant is a historical term for the region around Syria and includes Lebanon, Israel, Palestine and Jordan. White House officials have said that "Levant" is a better translation for part of the Arabic name, al-Sham, which refers to a chunk of the western Middle East near the Mediterranean.

Many news organizations prefer the term Islamic State group because "the word 'state' implies a system of administration and governance," David L. Phillips, the director of the Peace-Building and Rights Program at Columbia University, told the Associated Press. "It's not a term that would be used to characterize a terrorist group or militia that is merely rolling up territory."

The AP recently decided to use the Islamic State group "to avoid phrasing that sounds like they could be fighting for an internationally recognized state."