Precisely. And for large portions of the last 1500 years the two civilizations didn't really interact. While the enlightened, democratic and liberal West prospered in Europe and later America, Islam, backwards and barbaric, continually devolved, miring itself in poverty and ignorance in the Middle East and Central Asia.
Now we live in a global world and these two cultures are clashing in ways not seen since the Crusades. Islam, reeling from an inferiority complex is lashing out at the West, certain in spirit that our wealth is undeserved because we are such a decadent culture of infidels and the world had in fact been promised to them by Allah.
The radicals among them feel that their poverty and powerlessnes is punishment from Allah for succumbing to Western influences and the only way to win back the good graces of Allah is to destroy the West. There are large numbers of young Muslims in France who while wearing hip-hop clothes and listening to rap music agree with this.
I think so. As I understand it, the nineteen 9/11 hijackers shaved off their beards, visited prostitutes, and did a number of other forbidden things, probably confident that their final act would square things with Allah and earn them their quota of virgins. In fact, the more they succumb to western music and culture, the guiltier they feel, and the angrier they get with us for corrupting them.