User blog comment:Nerdvana/Katana, Ninjato and the meaning of words/@comment-93957-20190526071718

Katana in this context is shorthand for uchigatana (打刀), As stated in the opening paragraph for the Japanese Wikipedia page for it:

"Commonly, the uchigatana has been referred to as "katana" following the Muromachi period."

Frankly put, if you say katana in Japan, it's going to be understood you mean that specific weapon. The Japanese have been calling it that since the late 1500s.