What is in a word?

In Somalia, there is a steady encroachment on key towns and ports, thanks to a militia belonging to a group called Shabab.

But what do you call the militia members as a group. If you are the LA Times, you call them islamic insurgents, but on the other coast, the NY Times calls them islamist insurgents.

According to religionstylebook.org, there is a difference, and an islamist is using a fundamentalist interpretation of Islam to further a political agenda, whereas Islamic is a more general-purpose adjective.