Just like how Japanese is completely different from English, JSL is completely different from ASL. For one, JSL uses mouthing to distinguish between various signs. ASL uses mouth movements a little bit, but not mouthing to this extent.
Fingerspelling is also used more in JSL than it is in ASL. Finger writing (drawing Japanese characters in the air) is sometimes used in JSL. Finger writing is never used in ASL.
JSL also uses the topic-comment pattern of sentence structure that is used in spoken Japanese as well as American Sign Language.