The wikipedia has a great entry on diatonic vs. chromatic:
http://en.wikipedia.org/wiki/Diatonic_and_chromatic
As the article says, these two terms are most often used in pairs, because they mean very different things.
The section on “modern meanings of diatonic scales” is particularly interesting to me, because it confirmed my suspicion that there is no generally agreed convention with regard to whether the melodic and harmonic minor scales should be considered diatonic. They are not in my book, because you can’t play them on a folk harp.
I actually like what the Harvard Dictionary of Music says: basically that diatonic refers to the white keys of the piano. This is where I learned the mode system, and I think most students get it this way too. It’s really fun to hear each of the diatonic “Church Modes” over a Root-5th-8th drone in the left hand.
On the mountain dulcimer, we have to remember that the 6+ fret, which is added to most modern dulcimers, changes the game a little bit, as does playing across the fingerboard as opposed to just going up and down the melody string.