A concertina is a free-reed musical device like harmonica and accordions. It has bellows as well as buttons specifically on both the ends of it. When this instrument is pressed, buttons travel in same direction as bellows unlike the accordion buttons that travel vertically to the bellows.
Concertina was developed first in Germany and English. The German version was invented by Carl Friedrich Uhlig in 1834 whereas the English version by Sir Charles Wheatstone in 1829. Different forms of concertina are used for polka music, tango, classical music and traditional music of England, Ireland and South Africa.
However, since this musical instrument developed contemporaneously in German and England, types have been divided broadly into German, Anglo-German and English.
German concertina: It is larger than Anglo or English concertina. It is usually bisonoric, makes use of various styles of long plate reeds and is square in shape rather than hexagonal. Unlike Anglo and English, A German concertina may sometimes have more than a reep per note producing that vibrato effect.
Anglo concertina: Anglo-German or Anglo concertina is basically a hybrid between German and English concertina. Button layouts are usually same as original 20-button German concertina. After a few years of its development, the German concertina became a popular import in Ireland, North America and England because of its fairly low price and ease of use. The English makers responded to this by providing their own versions using English processes-concertina reeds rather than long plate reeds, hexagonal ends and pivots for every button resulting in the contemporary instrument.
English concertina: It plays a chromatic scale and is unisonoric with every button producing the same kind of nore whether the bellows are pulled or pushed. The instrument is smaller than German concertina and is hexagonal, although it often has eight, ten or twelve sides. The concertina alternates note of the scale between the two ends, allowing quick melodies. Sir Charles Wheatstone must be given the credit to have patented such a design in England.
You can get these different instruments over the web. There are many websites that sells them. Just make sure to buy from a reputed and reliable seller. I recently bought an Anglo concertina from All About Accordions and Concertinas. I got it at a very reasonable price from there. If you stay in Ireland, I would really recommend you to buy from this site. They provide quality instruments to their customers.