This article is from the Concertina FAQ, by Chris Timson firstname.lastname@example.org with numerous contributions by others.
These should be included in that, even though they have a totally
different evolution to Charles Wheatstone's invention, their players
refer to them as concertinas. Indeed many of them have the word
"Concertina" designed into the fretwork on the ends in very large
letters! In fact the Chemnitzer concertina was invented in 1834 in
Chemnitz in Germany by Carl Friedrich Uhlig. He called his new
instrument the "Conzertina".
It is related to the bandoneon, being approximately the same size and
shape, square or slightly rectangular; the treble end of a Chemnitzer
concertina usually has three rows, and in layout is not unlike an anglo.
The bandoneon however has several different layouts, both chromatic and
diatonic; the treble end probably has five or six rows. I know of only
one player in the UK, though there are many more in North and South
America. The construction appears to be accordion like, as is the sound.
The Chemnitzer concertina is particularly popular among players of polka
music originating in Poland.
Steve Litwin's Home Page (see section 12) has lots of additional
information about this instrument.
There are probably other systems around - concertina makers and players
of the 19th century were a very inventive lot.