It seems to me that the UK/Irish people use a four string banjo while the Americans (except Mexicans who won't touch the thing) use a five string. That might explain the price difference.

There is also a six-string banjo. It is tuned like a guitar and was used in jazz bands as a rythm instrument. The banjo has less sustain than the guitar; but its attack is (or seems) louder. I am not sure they are still being made.

There is also the gut strung banjo--usually five strings. You can really play tunes and complex pieces on it quickly because it offers little strain on the fingers and you can barre easily. I haven't seen one for years.

Murray