Open-back banjos are normally associated with a popular style of banjo playing called clawhammer. Clawhammer banjo is normally associated with a genre of traditional music that is different from bluegrass that is called Old Time Music, Old Timey, folk or traditional Appalachian music.
Open back banjos generally have a mellower tone and weigh less than resonator banjos. The clawhammer models often have what is called a scooped neck which takes out the highest five frets of the banjo neck. This is done to make it possible to play "clawhammer style" closer to the fret board and forward of the pot or round section of the banjo that has the drum head on it.