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The C major and C Ionian scales are the same scale, we have just taken to calling Ionian major. It's the same way that the c natural minor scale is the same as the C aeolian scale, we just call it by a different name.
The modes of C are the 7 arrangements you get from starting the C major scale from its 7 different root notes. You only think of parrallel modes like you have described as a harmonic / composition technique to slide around keys or add interest to a piece.
Unfortunately, or for simplification (if you know what is what), scales and chords (which are completely different things) are named with the same name system. The "chord signature" A names the chord consisting of the tones 1, 3 and 5 of the A major scale. The "chord signature" Cm names the chord consisiting of the tones 1, 3 and 5 of the C minor scale. Because the "chords of a scale" must use ...
Notes do not "start" with C; C major is just the easiest major key to notate in modern notation. The concept of a major key came about long after letters were assigned to the notes. Before there were major (and minor) keys, people used modes, usually just using the notes of the modern white keys and starting and ending in different places.
Of course that could be a very interesting thing to do, but (assuming from your question about D major that you are a beginner) it would be better to wait a while before you try to do it.
In that case, you transpose up 200 cents, i.e. two semitones. G minor has the same key signature as Bb major, and the distance from Bb to C is two semitones.
Strictly speaking C major doesn't exist as a named scale, it is a chord. What you are thinking of is C ionian, which is the "root position of the scale" of a total of 7 "inversions" which are the modes.
It's quite easy to "construct" the major scale by adding perfect fifths (and adjusting octaves to keep the resulting frequencies close together). Start from C, and you get (in this order) G, D, A, E, H and F sharp, which is the entire G-major scale. (To get C major, you have to start from F instead.)
Given that the minor second intervals in both C major and natural A minor are the same, the chord on the fifth degree of A minor is normally going to be a minor chord, E min, with G as its third.
For the purposes of this question, chords are most usefully defined as every other note from the root of the chord, with chords having their roots on each note of the corresponding scale. Triads (3-note chords) Given a major or minor scale, the chords, given by the scale degrees comprising each chord are