This is a question I asked myself after a reader in the UK wrote me about one he owned. Turns out that in the 1800s, after the banjo made it across the pond to England and got established through minstrel shows, etc., someone tried a different playing style that required a resonator to boost the volume. (At that time, almost all banjos were "backless.") The instrument caught on, but it was built and played differently than banjos in North America. A few found their way back to North America. When I've heard about individual specimens folks found in their grandpa's closet or whatever, I assumed they were "one-offs" or custom jobs. But as it turns out - duh - England had a whole industry and a number of popular musicians as a result of this instrument.
At first glance, Zither banjos look like six-string banjos with resonators and slotted heads. I'm wondering now how many of the old "six-string banjo" photos I came across when I was rehearsing six-string banjos are really Zither banjos. (I know Johnny St. Cyr played a REAL six-string banjo, so I still believe in the thing as a Jazz instrument, though.)
The English banjo manufacturers used the design of a slotted guitar head and attached six tuners, three on each side. The first four string are more-or-less the same as the first four strings of any four, five, or six string banjo, different tunings aside. But the fifth string went down into a tunnel at the nut and came out at the fifth fret. THAT's why you never see the fifth-string peg sticking out on these banjos. That said, you can tune most zither banjos like a traditional North American 5-string and play them with traditional North American picking styles if you want to.
What about the sixth tuning peg, the one I haven't accounted for yet? It was almost never used. In fact, some English banjo manufacturers tried just using two pegs on that side of the banjo head, but would-be buyers thought those banjos looked funny, so the "dummy" peg was restored.
A few manufacturers experimented with putting six strings on the thing. The first five were roughly similar to the first five strings on a guitar (barring tuning differences, of course). Then the SIXTH string would come down through the tunnel and pop out at the fifth fret.
When I wrote my first article about 6-string banjos, a couple folks reported that they had this configuration. Now I know that they may have come from Britain or have been based on a British design.
Most of these that still exist still have they original vellum (scraped calfskin) heads. Folks who collect and play them try to replace the heads with vellum, so they have a distinctive sound, even if they're played "American-style."
The other thing that distinguishes them IS the picking style, which seems most often to use the thumb and first two or three fingers (depending on the artist), but never uses picks. There also seems to be more of a focus on melodic playing, almost like, say, a European mandolin (sans pick). Sorry to be vague, but some of the nineteenth-century descriptions are a little, shall we say, ambiguous.
A nice English fellow named Derek pointed me to this concise account: http://www.shlomomusic.com/zitherbanjo.htm
A more complete resource is: http://www.zither-banjo.org/pages/home.htm
Buried in its pages are several very old recordings of the thing being played by "serious" zither banjo players. Plus at least one explanation for how the things got their name.
I'm not saying to rush out and buy one. Just that they do exist and were once VERY popular in England and places like South Africa, so if you come across one of these in a music store or museum in the US, know that it's just our banjo's "English cousin," with its own - relatively respectable - history.