This a great question. There are many differences between traditional hazards like natural disasters and terrorist attacks. Let me name a few of them.
First and most importantly, terrorist attacks are immoral and evil. This is to say that terrorist attacks are premeditate to create fear and as much destruction as possible, such as the attacks on 911. It is rooted in hate and the worst of humanity. When it comes to natural disasters, there is nothing immoral about them. Natural disasters might cause more damage and death, but it is a natural part of life.
Second, with terrorist attacks, people cannot really prepare for them. Terrorists attack whem people least expect them. With natural disasters, there usually are some warning signs. For example, in earthquake areas, structures are fortified in a special way. There are also national agency that seek to bring relief and the like.