The Globe's Ombudsman Richard Chacon has a great quote from the paper's Washington bureau chief on why it refers to domestic spying as, well, domestic spying:
We've used spying, wiretapping, surveillance and probably a few other terms to describe Bush's NSA program. In the first few stories we explained in detail what was known about the program (the monitoring of overseas phone calls by Americans, etc.) and what was not known, such as the extent of the surveillance. Since then, the story has become broader -- a test of presidential authority in wartime, as applied to torture, the Patriot Act and detainee policy as well as the domestic spying program. In these broader stories, we needed a shorter way of describing the NSA program and more or less settled on "domestic spying."
We emphasize domestic because there are different sets of laws governing wiretapping of Americans and foreigners, and it's only the domestic side of these phone calls that has raised a furor. If we called it "spying on international phone calls and emails," or something like that, it could disguise the real issue. It could also cause confusion, as in sentences like "Senate Judiciary Committee Chairman Arlen Specter said he had "grave doubts" about President Bush's spying on international calls. . .," since the claim is that Bush has violated laws governing domestic surveillance.
As for spying, I think it's the clearest and most easily understood term. Wiretapping is not quite broad enough because the surveillance includes emails. Surveillance and eavesdropping are fine by the dictionary, but seem a little esoteric to me. Given the complex and legalistic subject matter, I think we should strive for the most easily understood term. (And while surveillance may be a less loaded term than spying, I'm not sure that's true of eavesdropping -- it sounds more polite, but no less intrusive.)
It's clear, it's called domestic spying because the targets are Americans (even if the call is being fielded or sent to someone internationally. That's all the explanation you need. The Bush administration's semantic push was a clever idea that sort of blunted momentum on the story, but it should be settled now, and the pressure has to be reapplied. I mean, really, did anyone buy that whole "It's not really domestic because that's not what it says on phone bills" bit?