Melodic style banjo is a style of 3 finger 5 string banjo playing that was created in the early 1960’s by banjoists such as Bill Keith and Bobby Thompson so that they could play note for note fiddle melodies. While Scruggs style is the most popular style of playing the 5 string banjo and gives great drive to bluegrass playing, this style does have its limitations. Mainly that you cannot play melodies note for note that are very intricate such as fiddle tunes.
When I was learning how to play 5 string banjo, there were 3 main styles of 3 finger playing - Scruggs Style, Reno Style, and Melodic or Keith style. Today one might argue that there is a more modern style called Fleck style - but that is for another conversation.