That's a Wodao and it is related to and at the same time, might or might not be katanas. Given that wodaos were used by pirate gangs comprised of Japanese, Chinese, and Koreans crews (a single ship/gang can have all 3 onboard). I guess the best way to tell them apart is to look for the hamon (wavy pattern) on katanas (which is a product of their forging technique).

TL;DR: The sword she is holding probably isn't a katana.