Chromatic harps are ones where you can have all the notes available all the time. These include the cross strung harp and the triple strung harp. The cross strung harp has two rows of strings that correspond to the white keys and black keys on a piano. They cross in the middle so the player has access to all the notes with both hands. Reaching up for the natural notes with the right, and down for the same notes with the left.
Like the cross strung, the triple strung is a chromatic instrument. The triple strung harp has two rows of diatonic (think white keys on the piano) tuned strings with a row of accidentals in the middle. It is not easy to play those middle notes, so players end up playing in the modes (d Dorian, e Phrygian, etc.) and using the middle notes just for accidentals.