What are the men fighting about in Treasure Island? What is the connection between the men wrestling on the ship and the boisterous singing on shore?

The men on the hunt for the treasure are in a fight because there has been a mutiny on board the Hispaniola. The two groups are fighting because Captain Smollett and his men are trying to survive, while Long John Silver and his men are trying to take control of the ship and the island. Jim fights for Smollett because he believes that Silvers is evil.
The connection between the song on the shore and Jim’s wrestling with Isreal Hands on board the Hispaniola is Jim’s decision to stay on Captain Smollett's side of the conflict. Jim tries to cut the Hispanola loose so that it will drift away and Silver’s men will have no way of getting off the island. While he is waiting and trying to cut the ship’s line, he hears the pirates on shore singing, and he realizes why he could never side with them,

And I thought it was a ditty rather too dolefully appropriate for a company that had met such cruel losses in the morning. But, indeed, from what I saw, all these buccaneers were as callous as the sea they sailed on. (Chapter 23)

The pirates are cruel and quick to turn on one another. Jim realizes that they don’t care for each other. Instead, they can easily overlook their allies who have died because they only really care for themselves and their fortunes. Jim ends up wrestling Isreal Hands because he sneaks onboard the Hispaniola and has to fight the pirates to save the lives of his friends and allies.