This is not right. The modes of the major scale each have 7 notes; instead you have listed both scales as having all 12 possible pitches, but just starting on different notes. You have listed a chromatic scale on C and a chromatic scale on D.
Also, the way you describe a number of the intervals is not correct: for instance C-F# is a 4# (in your notation).
As different modes have the same number of notes, you can think of them as having the same degrees (eg. I, II, III etc.), but the intervals between them are not the same. It is the different intervals produced between the different degrees of modes which gives them their character.
Using your notation, C Ionian and D Dorian have the following notes:
C Ionian (C Major):
I II III IV V VI VII
C D E F G A B
1 2 3 4 5 6 7
D Dorian:
I II III IV V VI VII
D E F G A B C
1 2 b3 4 5 6 b7
Really, the flat intervals above should be called minor intervals (m3, m7).
So, as you can see, the notes are the same for C Ionian and D Dorian (as you said!), but the intervals each degree creates with the root notes (C for C Ionian; D for D Dorian) are not the same.
It would be interesting to see where you got the information about these modes from; it is pretty far from accurate!