御伽噺[otogibanashi] fairy-tale
仕形噺[shikatabanashi] talking with gestures
人情噺[ninjoubanashi] love story

噺家[hanashika] professional comic (rakugo) storyteller
辻噺[tsujibanashi] stories (esp. war stories) or lectures told by someone near a road or temple while begging for money
三題噺[sandaibanashi] performing a rakugo story on the spot based on three topics given by the audience