I have been reading through the content of this site and forum on music theory. Most things I understand but there is still one area that leaves me cold. You probably guessed it, that good old chestnut, "modes."

If you play in the key of C major in a parallel mode (and it doesn’t matter which one) but lets say for example in the Dorian mode. It then follows that the 3rd and 7th intervals of the scale will be moved down half a step so you would have a flat 3 and a flat 7, in this case E flat and B flat.
The notation will show the key signature as having 2 flats (E and B), which is essentially, the key of B flat.
So why is this called C Dorian and not B flat? If I were to take a major scale form (the E shape) and start it with root note on the 8th fret E string I would be playing a C major scale. Now if I were to drop that shape down 2 frets, what would I be playing, bearing in mind that I could cover 2 octaves over the 6 strings, B flat major or C Dorian?
Is it really as simple as “it depends on which note you start with,” would a solo piece played in C Dorian always have to start on the C note?
Apologies for any blatant stupidity but somewhere along the line I am not getting to grips with the concept (or the Point) of modes.