Wahhabi. Which is a Salafist offshoot of Sunni Islam. Named after Wahhab, who was the last person to actually codify this variety of Islam.
Salafism itself has a (rather narrow) range of views. But all have the attitude that the earliest forms are Islam are the purest.
The IS don't so much kill those with inferior revelations or that have gone astray as require their subordination. They are intolerant of those who have rejected even inferior revelations, however, although absolute subordination can get you some acceptance. What you absolutely can't do is reject their domination: That is a declaration of war and violation of any contract of peace that could exist. In Darul Islam there is only pure Islam in charge; all others must submit in order to allow peace. Otherwise it's all darul Harb, the "world of war." Rather absolutist that divide.
IS is consistent with this. As they spread, they leave in peace groups that do not raise their hand against them. As soon as the US drew blood, their US captive was beheaded. As soon as Japan allied with IS' enemies, ditto. This is a consistent ideology and rational according to its own views.
India has scant Wahhabism. The local variety of ultra-pure Islam in South Asia is Deobandism. There's a lot of overlap. They're not incompatible. Sometimes it's hard to tell one from the other, since they drink from the same wells: A literalist interpretation of the Qur'aan based on a literal interpretation of the Sunnah combined with a predilection for considering the gates of ijtihad closed and favoring older, necessarily more Salafist interpretations. As far as I know both are okay with the various fiqhs. In recent years some madaris have mixed the two, and some have gone full-blown Wahhabi, mostly because of the need to be in compliance with the demands of their funding sources or because that's the teaching materials the madaris have. Afghanistan under Taliban rule was more Wahhabi than Pakistan and India.
But I'm just a former translator and high school teacher with just the usual background knowledge common to every American.
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