The five string is the older instrument. It seems likely that all banjos from thier African origins had a drone string but the total string count is debatable - probably a 4 string instrument but with one of those strings being a shorter one.
Later, late 19th century I think, with plectrum playing and with steel strings, some players did drop the 5th string. This would give what is effectively the plectrum banjo.
The shorter scale tenor banjo (also named tango banjo) did not come into being until somewhere around 1915 - that sort of WW1 era.