Yes, all that is true. However, it may be noticed that in this day and age, islam is the only religion used to justify attacks on civilians, sometimes as an end in itself. Yes, there can be terrorism (as you defined it) without any religious affiliation. LTTE was not motivated by islam. But it is a fact, no matter how much some muslims (I don't mean you) may try to pretend otherwise, that no other religion commands so many people willing to die for what they consider a religious duty.
The reason islam is associated with terrorism today is precisely because of that - yes, many terror attacks have political goals, but it is an incontrovertible fact that many of the foot soldiers are motivated by the hope of martyrdom and paradise. In other words, it is not merely a political or military duty for them, BUT A RELIGIOUS ONE AS WELL.