The small difference between John’s notes and mine might cause some confusion, so thought I would clear that up. However, the risk is that the full explanation might be even more confusing but here goes.
As stated above the extended 9 chord is a 9th scale note added to a 7 chord. The question is then should it bearded a maj 7th or a dominant 7th, ie in the C root, should the notes be C E G B D or should it be C E G Bb D?
The answer is that both are legitimate chords, and technically should be distinguished by the chord name on the lead sheet. CM9 or Cmaj9 infers building on the maj 7 ie the B in root C, while C9 infers using the dominant 7 ie Bb in root C as John has correctly shown.
In reality though I am not sure that all lead sheets reflect this accurately, and I seldom actually notice, because the original use of a lead sheet was as a basis to build your own arrangement, so you are guided as much by the sound, or the obvious chord progression. And many times anyway, the chord extension note, is only mirroring the melody, and doesn’t need included in the chord.
But that has changed a bit with the use of arrangers where the lead sheet is often used more like sheet music would be, and followed verbatim, letting the style dictate the arrangement, playing exactly the lh chords verbatim as written. So in that case, using John’s shortened chord, C9 would be C D E Bb, while CM9 would be C D E B.
No such distinction needed for minor 9 chords where the 7 scale note is always flattened, so Cm9 is C D Eb Bb.
The problem with writing all this down is that something that is essentially simple can start to seem very complicated🤐
Mike