The common feature of all the European Board Zithers is the diatonic finger board; the earliest iconographical evidence for this would appear to be the instrument Praetorius illustrates as a 'Schietholt' although other authorities (Hortense Panum for one) would trace this instrument (which she somewhat bafflingly calls a 'Balk Monochord') back to the monochordal 'canons' of Pythagoras!

So much for the history; the reality is a fairly ubiquitous distribution throughout Europe, from the Hungarian Citera to the Norwegian Langeliek (and Icelandic Langspil), taking in the French Epinette des Vogues & the Swedish Hummel on the way, and more besides, which would at least imply an ancient origin even though the evidence is a bit thin on the ground.

All these instruments have a diatonic finger board, although on the Citera, this is augmented by a second row of frets giving the 'missing' notes of the scale without detracting from the character of the diatonic fretting. Like the other European board zithers, the remaining strings are drones - up to twenty over three octaves (!) - which means you're fairly limited as to what key you can play in, unless you buy another Citera (I have two on the go right now...)

Essentially ZITHER is a category of stringed instrument in which the strings run the full length of the soundbox - so this includes the psaltery, Appalachian Dulcimer, Langeliek, Humel, Epinette, Citera, Hammer Dulcimers, Kantele, Santur, Koto, Kanun etc.

Being an American instrument, I would assume the Appalachian Dulcimer derives in some way from the European Board Zithers - certainly there's a lot of discussion about this on line. To this end, I've recently joined a Dulcimer Forum which you might be intersted in:

Dulcimer Player's Forum

And not forgetting the venerable Nonesuch Dulcimer Club

Have fun!