I don't think they give a stuff what we call them, they are capable of inflicting great damage on Nations who oppose them, especially developed trading nations.

I agree wholeheartedly with Lonesome EJ, there is huge destabilisation in the area and the answer will not be found purely through military means.
Much of the Muslim world, not just jihadists, see Western society as debauched and immoral, our way of life and governance offends ordinary Muslims so much that they are very reluctant to integrate into our society... there is a huge cultural gulf.