If you have C scale, C, D, E, F, G, A, H, C this is already Ionian. C dorian scale is when you play same tones but start from second tone, in this case D. I am correct?
You are correct that D dorian is the same notes as C ionian, e.g. you start on the second note. As for the other modes you can generate them by starting the ionian on a different note. The seven diatonic modes are related to Ionian as follows.
Note ........ Mode
1 ........ Ionian
2 ........ Dorian
3 ........ Prygian
4 ........ Lydian
5 ........ Mixolydian
6 ........ Aeolian (natural minor)
7 ........ Locrian
Writing a melody in one of these modes does not necessarily sound like a tune written in the relative "Ionian" or major key. The reason is that each mode emphasizes different tonal centers as one plays patterns in each mode. Clearly, if you play the D dorian mode by continue to search for C, E, G, and B to play them at the beginning or end of phrases or on string beats you will just create a C major sounding tune. Some of these modes have an ethnic historical context dating back to ancient Greece (or other European countries or regions). The fact that they are all related is nice and makes the patterns easy to remember but each has a distinct character.
To illustrate the later consider playing the opening line to "Joy to the World", which is just a descending major scale. Do it C on a piano or other instrument. Now play the same phrase, rhythmically, starting on C but descending on each of these modes.
A similar device can be used on the Melodic minor scale to generate related modes.
I hope that helps somewhat.