There are thousands and thousands of pieces composed or arranged for classic banjo.
"Ragtime" would be a genre inside of classic banjo, the same as marches, schottisches, polkas, jigs, reels, hornpipes, waltzes, mazurkas, cakewalks, foxtrots, song and dances, characteristic pieces, intermezzos, novelty.
Ragtime is a part of classic banjo, but just one part.