A dominant ninth is a dominant chord with a ninth, but that’s not what a major ninth chord is. The major ninth chord (or just ninth chord), as an extended chord, typically includes the seventh and ninth along with the basic triad structure. Thus, a Cmaj9 consists of C E G B and D . When the symbol “9” is not preceded by the word “major” or “maj”, the implied seventh is a dominant seventh—e.g. a C9 consists of C E G B♭ and D.
An added ninth chord (add9) is a major triad with an added ninth. Added ninth chords are different from other ninth chords (9, maj9) because the seventh is not included. Read More »Added 9th (add9) Chords (Closed Position Shapes)