Not quite. D Dorian is derived from the C major Ionian mode certainly, and in this way can be seen as directly related. It is often, in fact, thought of as a permutation of this tonal centre, and is fruitful to think along these lines when considering modes. Many often confuse modes for scales and vice versa, and while they are theoretically very similar if not the same, it is when you go down to it that you realise that they are in fact very different, and that the former is wholly indebted to the latter. A mode, instead of being a scale in its own right, is, instead, a permutation of a scale. More often than not, the modes are worked out in relation to the major scale, this is really where all western classical notions of harmony and what sounds right to our ears comes from after all. The Ionian mode is, in fact, this very same major scale. So, if we were to say that something is in D Ionian, we would be saying that it simply uses the D major scale throughout, without any variation.