The two major branches of Islam are the Sunni and the Shiite branches; there are other subsets, such as Wahhabi which is strongly present in Saudi Arabia. Osama bin Laden was Wahhabi.
Islam is more than just a religion; it is a theocracy, so it combines both religion and government (for lack of a better term at the moment); that is, one of the goals is to have sharia, or the moral code and religious law as the law of the land. There is much ongoing discussion of sharia, for example, in areas (such as France) where there are large concentrations of Muslims. There are areas where allegedly neither the police nor the fire crews will go in parts of France.
Sharia covers not only crime, politics, economics, sexual intercourse, hygiene, diet, prayer, and everyday etiquette and fasting.
So, to a certain extent, it is correct to say that ISIS is on a political bent using war as its means of spreading and enforcing it’s view if Islam. It is also, at the same time, a religious war, based on religious principles, including the formation of the caliphate, a form of political-religious leadership which centers around the caliph - the “successor” to Muhammad, with overtones of world-wide domination under the caliph.
Saying that Islam is ISIS and ISIS is Islam is the equivalent of saying that the Catholic Church is Christianity, and Christianity is the Catholic Church.
To add to the confusions, ISIS appears to have started as an al Qaeda affiliate in Iraq before it crossed over into Syria to join the conflict there. Once in Syria, they ended up in conflict with Al-Nusra front, and al-Qaeda affiliated Syrian rebel group. There should be no surprise that people are confused as to who is who, and what relation they have to whoever else is who.
And in the process, they are causing Christians and others to flee, and a number of those who have not fled have been executed. Children have been beheaded. They have doubled back into Iraq, taking a number of cities.
And they seem to be recruiting young men world wide; as one person noted, we are trying to stop them and we can’t kill them as fast as they are recruiting.