Wasburn is an American firm which started making guitars, mandolins, banjos, mandolin banjos, banjolins, banjo ukuleles and zithers in 1883 in Chicago. Originally, it was a division of Lyon & Healey and instruments badged Washburn were their flagship line.
Often cited as a company of George Washburn, there doesn't appear to have been any such person. George Washburn were the first names of Lyon.
In 1928, the fretted instrument patents and machinery was sold to another chicago company - J.R. Stewart. In 1930, the name was sold again to the Tonk Brothers.
Today, the Washburn brand still exists as a guitar, mandolin and banjo brand (as part of U.S. Music Corporation which is the parent company for other brands such as Framus and Oscar Schmidt) but it appears that most instruments are now made in China or Korea by Samick:
The modern Washburn banjos are prefixed "B-" with B6 being a 6-string, B7, B8, B9, B11, B14, B16, B17 and B120 are five strings in various specifications. Vintage Washburn models tend to have numerical designations along with names such as Professional, Presentation, Melody, Improved and Models 421, 422, 442, 565, 5100. This is not an exhaustive list as the details are not readily available.