I recall having a conversation similar to this one recently, in another forum. The answer I was given went something like this:
In Korea today, there are two very different styles of sword arts. One is kumdo, which is basically Japanese kendo. There are a few subtle differences, I'm told, but basically, it's kendo.
Then there is gumdo - more often called haedong gumdo. The Korean character that is pronounced 'k', I believe the name of it is 'giok', can also be pronounced as a 'g' - lots of lingusistic terms could go here, but I'll settle for that. Practitioners of haedong gumdo (HDGD) will generally spell it with a 'g' in English to distinguish the two arts.
HDGD is generally practiced with a live blade for most techniques. Drawing and cutting etchniques are taught, and sparring is included in the curriculum, though not with live blades, I'm pretty sure. The focus of HDGD is on mass battles, though, and on battlefield strategies.
I didn't want to feel stupid when posting this, so I found this site:
http://www.stormpages.com/haidonggumdo/
It has much more information on the art than I could present here.
As for them using katana... well, the curved blade is an excellent design for cutting and slashing weapons. Hard to get around that.
Of course, there's also the school of thought that the Koreans developed the sword-making technology that made the Japanese famous...
