Wahhabism vs the Muslim Brotherhood

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this is quite an interesting division between Islamists that you can see a lot in the Middle East, most recently as one of the sticking points in the Qatari-Saudi dispute, but also in Egyptian politics, the Syrian civil war etc etc. Keep in mind that the while this division has always been there, there was significant cross-breeding during the twentieth century, which means both movements share blame for violent jihadis.

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isn't "Wahhabist" one of those things no one actually calls themselves?

Trouble is there isn't really a better way to describe them without being too broad (e.g. Salafi would include MB itself) including what they call themselves.

Whichever one is less religious?

They both are very religious, given they are religious organizations. The difference is that the former strive towards purity, respect for leaders and idealised vision of the past,while the latter are normally very politically charged, have a lot of rhetoric that borrows from previous social activist movements in mena etc. The former is more of a subculture that works in tandem with the state, the latter are populists who promise to create a popular Islamic state through democratic (of sorts) means.

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'Wahhabism' isn't a thing.

Trouble is there isn't really a better way to describe them without being too broad (e.g. Salafi would include MB itself) including what they call themselves.

No it wouldn't. In fact the Salafist parties initially backed the coup against the Brotherhood in Egypt.

They still back the coup, as far as I know. My point (which admittedly I completely mangled especially with the bit you bolded in parenthesis) was that there was a lot of overlap between Salafism and other Muslim movements, including the MB especially back in the day.