There're 3 companies operating maritime transportation between Fukuoka and Busan.
Beetle and Kobee are jet foils while Camellia is a regular ferry. Kobee and Camellia have 1 daily departures. JR Kyushu Beetle has 2 departures on regular season and 3 departures on peak season. Here, the peak season means either side of the straits is on public holidays. JR Kyushu Beetle and Kobee had code share agreement which terminated in March 2016.
There's no luggage check-in on Beetle and Kobee. All luggages must be carry in. There's one storage area on each deck and it also has overhead bin. Each luggage must be 158cm (h x w x d) 3 luggages can be allowed, including 2 free luggages. The 3rd luggage is charged at 1,000 yen. While on board, the staff asks the passengers for drink and duty free shopping. When the tide is 1-2m high, travel is very smooth. You might feel like riding a bus. On the other hand, when it reaches over 3-4m, departure may be conditional or canceled. The average speed is 80km/h. Near the northern cast of Tsushima Island, jet foil reduces the speed to avoid the collision with wild whales and dolphins. 60-70 % of the passengers are Koreans and 20-30 % are Japanese. Passenger deck staff speak Japanese and Korean, some English. There's no meal stand on board. You may order the staff for light meal and drink. Immigration queue should not be long on both end of the straits. Generally, the queue is only passengers on board with the same ferry.
This is the regular ferry. Luggage can be checked in with the additional fee. Second class passenger room is shared room by about 10 people at maximum and is separated by male and female. Upper class room Canberra shared by a family.
Prepare Japanese yen before you are on board to pay while you are on board for restaurant and vending machines. The ferry ride is about 5 hours. You'll depart at after noon from Hakata Port and arrive at Busan in the evening. On the other hand, although the boarding time in Busan is in the evening around 18:00, actual departure is after 10 PM. The ferry stays in Busan port since the immigration at Hakata port starts at 7 AM.