It's both, just like the fight in Israel is both and just like the fight in this country is both. The difference is W has a policy of going and finding them wherever they are with whatever it takes. We are the only ones committed to fighting world terrorism.
As you say, Putin has not supported us in the war against terror. He made a strategic miscalculation way back and needs to correct that mistake and come on board. To be honest, I'm not sure he knows how.
AS far as the terrorists in Chechnya, my view sees muslim terrorists in a simplistic manner. They may be in a different area trying to take over (or destroy) a different group of people but aside from that, they're ALL the same bunch of scum using the same tactics.
Fascism has many faces. This 'muslim fundamentalism' is simply the most recent face. Carter turned em loose, Clinton allowed em to grow with impunity, now Dubya's gonna try to clean em up. Once again a Republican has to clean up a Dim's mess.
Some things never change.