What constitutes as "war?" What constitutes as "organized terrorism?"?

For example, this “War on Terror” the United States and other allied countries have been involved in doesn’t seem to fit the traditional definition of war, usually defined (generally) as armed conflict between two oppossing states or factions within a state. From what I can tell, terrorists don’t necessarily have to be sanctioned by their home government to “start a war,” either. I’m not even sure if they have to have a known leader to be considered a terrorist organization. (And any of this is up for debate/discussion because honestly, the usual lines all seem a bit blurry from where I stand.)

I’m curious, then, about two things, making my question two-fold: (1) what, in your opinion, constitutes as “war,” and (2) what qualities might qualify the acts of one group (large or small) as “organized terrorism?” In light of the War on Terror, these two topics are very much connected in my mind.

I find this all fascinating in the sense that it is something that can be explored creatively, and has been and will continue to be explored, in fiction—namely novels and movies. As for the kind of answers I’m looking for: Links are great, but really I’m looking for more personalized answers and opinions to complement any “textbook definitions” that may be given. (I guess what I’m trying to say is that I need some broad perspective here.)