Interesting stuff these modes.

Another way of thinking about them is to start with a major scale such as D. If you go from the second note up to the second note (E to E) then that's the Dorian mode of D. It sounds like an E minor but isn't quite because it has a C# in it - that doesn't matter much because the E minor chord will work (E, G, B).

If you start and end on the sixth note, you'll get the relative minor scale, B minor.

Starting on different notes of the scale give you different modes and a different feel.

With a Dorian mode tune in D (E - E) you might find chords D, C, G and Em work well. The B minor tune on the other hand might feel better with Bm, Em, A and D. It's good fun to cross them as well because it creates a sort of ambiguity.