Now, Republicans seem to find the word "filibuser" toxic, so Inhofe also said "It's not a filibuster. I don't want to use that word." That's up to him, but reporters need to take note and be careful: it's not sufficient to ask Republicans about "filibusters." You might get spin, and not reality.
In the real world, however, what matters is what Cornyn said. It takes 60 votes to do anything in the Senate. That's true whatever they call it, and it's true whether or not anyone actually forces a cloture vote.
I wrote more about the Hagel situation earlier today, but again, this is really simple. Everyone covering the Senate needs to understand that Republican are requiring 60 votes for everything; that they've been doing so since January 2009; that prior to 2009, filibusters were frequent (since January 1993) but not universal; that very few Republicans have voted yes on cloture but no on the underlying substance on anything since January 2009; and that the name for requiring 60 votes is "filibuster."
And I'll remind everyone again: to say that something is being filibustered does not mean that it has lost; sometimes things are defeated by filibuster while sometimes they pass despite a filibuster. A bit trickier is how to write about whether "Republicans" are filibustering; I usually feel comfortable saying they are because all Republicans back the 60-vote standard even when they are part of the 60, but I could imagine other ways of discussing it. What is important to avoid is the notion that something was not filibustered, even if it had very few opponents; surely, those opponents were not simply opposing, but filibustering.