Thanks for your replies, guys.

Yes, Bardsley, your explanation did clear things up a bit for me. Why would playing a C major scale be either in C Ionian or Lydian?

So, for example, if I wanted to play a C Phrygian solo over a progression in the key of C, I would use the notes in the G# major scale - is this correct?

This does make a little bit of sense for me, because recently we were jamming to a classical piece in the key of E, according to the pianist, but nothing I was playing over top of it in the E major scale sounded right, until I switched to the C#m scale, and everything sounded nice.