added tone chord
The C9 (left) and Cadd9 chords.
For example, consider the C major triad, composed of C, E, G (the root note, the third, and the perfect fifth). If we add to this the 9th note (in other words, the second in the octave above the triad) we get the chord Cadd9 (or C+9). This is NOT the same as a C9, which is an extended chord (a ninth chord), and includes all the thirds up to and including the ninth. In other words, C9 comes with (an implied) seventh, whereas C+9 has no seventh.
Making the add11 and add13 chords follows the same process. There's no chord called add7 because this would be identical to the dominant 7th chord. The only other added tone worth mentioning is the 6th. Although adding the 6th to a triad gives an added tone chord, it's notated as if it were an extended chord. For example, if a 6th is added to a C major triad the resulting chord is called C6 not Cadd6 (even though Cadd6 would mean the same thing). The only difference between C6 and C+13 is that the 6th note in the C+13 is an octave higher than in C6. Certainly when it comes to guitar voicings there's very little difference between these two chords and C6 is mentioned a lot more often than C+13. In any event, both C6 and C+13 contain the notes C, E, G, A.