There's only one jetfoil route between Korea and Japan: Busan - Fukuoka(Hakata) which must be what you researched.
This route is co-operated by Miraejet's(Korean operator) Kobee+ and JR Kyushu's (Japanese operator) +Beetle. You could see some basic information in English on JR Kyushu website ( http://www.jrbeetle.co.jp/internet/english/index.html</a> ), but internet reservation can be made only in Japanese.
Korean counterpart website ( http://www.miraejet.co.kr</a> ) which is used for online reservation on Korean side, does not have English website either. You could view schedules in image files though:
February: http://www.miraejet.co.kr/SKD_Images/sch_201402.gif</a>
March: http://www.miraejet.co.kr/SKD_Images/sch_201403.gif</a>
April: http://www.miraejet.co.kr/SKD_Images/sch_201404.gif</a>
where the top block of rows represent "Busan to Fukuoka' and the second block of rows for 'Fukuoka to Busan'.
The 3rd block and below are shuttle runs between Busan and Tsushima Island (Japan) that may or may not proceed further to Fukuoka. Accordingly, you can ignore them.
Black dots represent the Kobee+, and white dots represent the +Beetle. Occasional black/white squares on the chart indicate that the jetfoil will make a port call at Tsushima Island, on its way to/from Fukuoka.
Fare on a jetfoil isn't cheap, one-way costs 135000 Korean Won, return trip costs precisely double that.
Overnight ferry destinations vary, you could choose the same Fukuoka, or Osaka, or Shimonoseki (Western tip of Honshu island of Japan, across the channel from Kitakyushu northeast of Fukuoka).
Therefore, Osaka overnight ferry gives you the farthest reach into the heartland of Japan, and it's operated by Pan Star ( http://www.panstar.co.kr</a> ). One-way to Osaka in the lowest, four open-berth compartment is 162000 Korean Won, but return ticket costs only 244000 Korean Won, not the double.
Sail to Osaka from Busan is 3 times a week, on Sundays, Tuesdays, Thursdays at 15:00. You arrive in Osaka by 10:00 next morning. Return trip from Osaka also departs at 15:00, but on Mondays, Wednesdays, Fridays.
Now that many low-fare airlines are participating in the market, jetfoil or overnight ferry may or may not an economical option for you, depending on how far in advance you plan your trip, which city in Japan you plan to visit in what order, and whether you'd be able to find a cheap flight ticket or not, because the competition for those cheap tickets is seriously severe and they get sold out fast.
