The Banjolin is an instrument the same scale length as a Mandolin, but with only 4 strings. It is essentialy a soprano banjo.
The Banjolin does not have paired courses like the Mandolin, Mandola etc. The related instrument which does, is called the Mandolin Banjo. Many sources confuse the two, but they are quite distinct instruments.
To understand the Banjolin, you need to understand the popularity of Mandolin Orchestras and later Banjo Orchestras in the early 20th century. The Mandolin came in first, but the banjo became increasingly popular. Out of work Mandolin musicians needed an instrument which was like the mandolin but constructed and sounded like a banjo. This gave rise to not only the banjolin, but the Mandolin Banjo and the Tenor Banjo as well
Actually, the confusion is understandable as the name of the mandolin banjo was undefined when it came into existence in the early 20th century.
Being constructed like a banjo, but strung like a mandolin led some makers to call them banjo mandolins or just 'banjo-lins'. To add to the confusion, a man named John Farris from Hartford, Connecticut had a patent on a banjo which he called a banjolin - but it came as Soprano, Alto, Tenor and Bass and probably 4 and 5 string versions (Quartette and Quntette) - this was in 1885!
There is no special history to the banjolin - it appears in catalogues of the main manufactures along with other members of the banjo family back into the golden era of banjo bands in the early 20th century.
Strangely, there is a type of bowed fretless zither called a banjolin (also there exists the guitar-o-lin and ukelin).