I was listening to Green Light by Lorde, during which there is a modulation from A major to the mixolydian mode. DOes that count as a 'key change' per se?
People have different viewpoints on this, but one prevailing view is that a modulation must change tonal center. In other words, a move from A major to A Mixolydian is not a modulation, because the tonic (=tonal center) is still A.
As such, we just call this a "change of mode."
A key change occurs whenever the key signature changes. This is pretty objective and quite different from a modulation, which can occur with or without a key change (often with accidentals). If you are switching modes but not tonal center, I would not call that a modulation; I would call it "borrowing (from a parallel scale)."
In the event of a modulation, the music is still with the same key signature, as modulations are generally a temporary move. With a key change, the term says it all - the key has changed, it's not temporary, there needs to be a sign displaying the new key.
'Borrowing', from parallel key and other modes with the same root - as in A major using A Dorian, A minor, A Mixolydian etc., is going to be a modulation, and there will be the necessary accidentals in place, with the feeling that the piece will eventually return to the original key. Other common modulations are moving to a related key, a fourth or fifth away, and relative major/minor changes.
Is this all about the use of a bVII chord in the final choruses? Just let it BE the bVII in the key of A. A chromatic chord doesn't necessarily imply a key change.
Think of a simple blues progression - A7, D7, A7, E7, D7, A7. You have no problem with that being in the key of A, despite the Cnat and Gnat notes do you?
This is another example of terminology trying to put hard and fast lines where none exist. If the "tonal center" changes for just one chord, it's not a modulation; if an entire movement is around a new tonal center, it's modulation. But everything in between exists as well, and there's no convention (nor could there be reasonably) to say exactly when "modulation" occurs.