The Islamic State, al-Qaeda and the Muslim Brotherhood all share the same goal: the imposition of Sharia over as much territory as possible, and ultimately over the whole world. But the Muslim Brotherhood is not working toward this goal with overt violence (except when it is), and so as far as Obama is concerned, it is “moderate.”
“Obama secretly backing Muslim Brotherhood,” by Bill Gertz, Washington Times, June 3, 2015 (thanks to Anne Crockett):
President Obama and his administration continue to support the global Islamist militant group known the Muslim Brotherhood. A White House strategy document regards the group as a moderate alternative to more violent Islamist groups like al Qaeda and the Islamic State.
The policy of backing the Muslim Brotherhood is outlined in a secret directive called Presidential Study Directive-11, or PSD-11. The directive was produced in 2011 and outlines administration support for political reform in the Middle East and North Africa, according to officials familiar with the classified study.