Islamic terrorists is not a defined enemy; many people are Islamic, and any of them could be terrorists. The list of who is considered a terrorist is secret and we are not privy to which people or even organisations are considered enemies in this war on terror. The US is also frequently attacked by Christian terrorists.
Terror aims to scare a population, but more importantly to drive a wedge between a government and its people by pushing the government into ever more repressive measures in an attempt to winnow out the terrorists, who can melt back into the population. The aim is precisely to force the government into ever more draconian measures which alienate the population and build support for the terrorists - to force the government to try to fight a war on the terrorists' terms. A great illustration of this from another era is the film The Battle of Algiers - torture, repression, removal of civil rights, and extra-judicial killing by the government in response are exactly what terrorism aims to achieve. Killing innocents in cafés is not the goal of terrorism, it's a means to an end, and that end is to force the government to adopt terror in response.
The correct response to terror attacks is careful police work to track down the killers and bring them to justice, so that they can't continue to plant bombs. This can be done within our existing legal frameworks.
The wrong response is to declare war on the the terrorists' terms, oppress your citizens, and kill yet more innocents in the cross fire as you target people on suspicion. Extra-judicial killing outside of war is as wrong as terror attacks, and as damaging for the parties involved, and eventually it comes to resemble terror itself.