Wrong.
C natural minor is the same scale as C aeolian, it can never be C ionian, which is C major scale.
And as far as melodic minor goes, the modes are:
I) C melodic minor
II) D phrygian #6
III) Eb lydian #5
IV) F mixolydian #4
V) G mixolydian b6
VI) A aeolian b5
VII) B alt (or "super locrian"),
spelled out (loud

),
I) C, D, Eb, F, G, A, B, C
II) D, Eb, F, G, A, B, C
III) Eb, F, G, A, B, C, D... I bet yougetthepicture.
The point is to analyze each scale from its root.
Also check out the chords (and arpeggios!!!) coming out of each scales, as they are more important playing-wise [arpeggio-based playing is basically playing chords over chords (not necessarily just min7 on min7, experiment!!!)].
For C mel min: I) Cmmaj7 II) Dm7 III) Ebmaj7#5 (#11) or Ebmaj7b5 IV) F7 or F7b5 V) G7 or G7#5 VI) Am7b5 VII) B alt or B7b9b5 or B7#9#5 etc... play all the arpeggios over respective chords, also play them over a C drone, concentrate, listen.
I guess that enough drivel for now.