hmn..i'm no expert in swords...but according to wikipedia: "shinobigatana, or the more correct term to use is ninjato, is a sword that ninja carries. Often, however, they were much shorter than the traditional daito katana used by the samurai of feudal Japan". See
http://en.wikipedia.org/wiki/NinjakenSo based on this, some shinobigatana or ninjato swords are classified as katana.
Azumi was trained by a Samurai Master. She was trained in martial skills of samurai and shinobi sword fighting, and the art of assassination.
Special thanks to Wikipedia. LOL.