Could this undermine our situation with Russia or another country when each country sees things differently as their own terror threats?It already does - need I remind you that America's unconditional support for the Israeli government (which is unarguable) and the Israeli government's perceived use of terror tactics in the Occupied Territories (which is arguable, but we're talking about perceptions here) is one of the major, if not
the major, reasons why America is currently such a terror target - from Islamic extremism, at any rate.
Is this War on Terror with enemies that are only our enemies?It is in all practical respects, and to an extent that is fair enough.
The problem is that the associated rhetoric coming from the Bush administration & their allies (and indeed with any country faced with any threat, justified or not) is couched in catch-all, dyadic terms of good and evil, freedom and tyrrany, and so on.
The bandying about of such words raises the perfectly reasonable question such clear-cut, absolute standards are applied selecitvely. Why are some evils and some tyrranies tolerated or even approved of (uncontroversial ones would include Sudan & Saudi Arabia, but also arguably Pakistan and Israel), and others are not (Afghanistan, Iraq, Libya)?
If we are saying this a world War on Terror should we consider other governments problems with terrorists and support them? No. You should condemn and act against the use of terror against civilian populations wherever it takes place, and
whoever perpetrates it - regardless of the status of the perpetrators i.e. be they terror groups or governments.
In effect, the definition of terrorism that we should be using is based on what constitutes an act of terror - direct targeting of uninvolved civilians or
acts of violence that do not discriminate against civilians*. It should not be based on whom is being attacked, or who is doing the attacking; nor on the whether the perpetrators wear a uniform, a headscarf, or a balaclava (sorry, ski-mask

).
*Note - some civilians may still be killed accidentally even if the actions are discriminating (which is where the hateful phrase "collateral damage" comes in). As a rule of thumb, perhaps we can say that if more bystanders are killed than intended targets, the action (be it a bomb, an armed assault, or a whole battle) is indiscriminate.
I'd say this second definition (acts of violence that do not discriminate against civilians) covers about half of what is going on in Iraq. The other half, that which is actively discriminated towards the security forces, is more usefully thought of as guerilla warfare, I think. The balance is made up of "direct targeting of uninvolved civilians", which is arguably the "worst" type of terrorism.