Karate sword? I do wonder if they are talking about a katana - a Japanese sword that is not connected to karate in any way, shape or form ... apart from all the strange people who like to pose with one in their karate uniform.
But hey, there are indeed karateka who also study real sword arts. However, these folks would probably throw up (or be insulted for life) if you used the term "karate sword" about a katana.
The weapon art of katana is most of the times called kenjutsu. Drawing the sword - combat style - is referred to as iaijutsu. These arts art a part of Japanese bujutsu (or bugei) - the old warrior (bushi) arts and methods of Japan.