Hi Ian
The C Add 9 means play a C chord triad which would consist of the notes C(1st), E(3rd), G(5th), and C(8th) but add a 9th - the next note to the top C, which would be D, so the ascending chord notes would be C, E, G, and D.
Often a C9 would be played as a C7,9 which would play as C, E G, B(b), D

The Dsus2 or Dsus4 is a suspended chord. It is a little different. DSus2 essentially means drop the 3rd and instead play the second note of the chord instead of the 3rd note. In a D Major Chord, the triad notes are D, F#, A (and D). A Dsus2 would be D, E, A, D. DSus4 would mean drop (suspend) the 5th and play a 4th, therefore: D, F#, G, D (or possibly just the notes D, G, D).

The musical intention of suspended chords it to make them sound like they want to (and usually do) resolve back to the normal triad. In other words, a CSus4 often resolves into a C chord (or similar variations).

In jazz, it's not illegal to use either variation of Csus2 or Csus9. This is because in jazz you can usually throw away the rule book (ha ha). Probably you can find useful information in a book entitled Rudiments of Music. I still use this book today, many years after my academic training (classical piano).

In summary Ian, you are actually on the right track.

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