Jolly:
Well.. I was trying to explain the modes a different way to hopefully shed some light on how they are constructed and relate back to the Ionian mode. I agree with what you said though.
If I say "E Phrygian" then I am not only defining the 3rd mode but also which Major scale that mode belongs to, so it becomes a scale: the E Phrygian Scale. However, If I just say "Phrygian" it's more do with the concept of modal theory.. well at least that's how I see it in my head. :D
I am only a relative newbie to music theory, so I may simply have my wires crossed somewhere. :)