The sight of the ship is not being saved, but a reasonable hope that you might be saved. And, while nothing you did brought the ship your way, you can do a lot to make your salvation a greater certainty by deliberately moving closer to the ship and cooperating with its crew.
Using the parameters of your story, the Protestant would not say "We are saved!", he would say "Hey, that ship sure looks a lot better than what I've got now, let's move toward it and make sure it's not full of terrorists." IOW, the Protestant seeing potential salvation far away is a seeker being led by God. If God graced him with the ability to swim he might be saved. Not everyone can swim. Once he is plucked out of the water onto a safe ship, he is saved. Then he leads the rest of his life in service to Christ and being sanctified. God will protect him and never allow him to ever be lost at sea again permanently.
BTW, if it had been me who saw the ship, and as an economics major, I would have simply assumed a cigar boat and sped toward the larger ship. Don't worry, I would have picked you up along the way. :)
Actually, everyone who is elect would say that, not just Calvinistic-Protestants.
The difference comes out when the story is later retold by the Christian who was rescued.
The reprobate would continue to paddle off thinking there is a better boat somewhere else.
Kosta's boast analogy pretty well defines what a Catholic or Orthodox person would thing -- by your reply, Forest, I guess you'd think along the same lines.
FK, I was using the ship as the "mark" Koloktoronis uses in his posts: our Lord Jesus Christ. The Protestants say "I accept Jesus as my Savior" and you consider yourselves "saved." The Orthodox/Catholic accept Christ and only begin the process that may lead to their salvation. We have to actively follow Christ and hope that our hearts will be changed so that we may conform to the likeness of God, so that we may be saved.
Thus, in my analogy here, the Orthodox/Catholic would actively work in the direction of their salvation. Your account of the Protestants is incompatible with the Protestant notion that salvation is "an instant" (when you accept Jesus as your Christ).
Hmmm....In the shipwreck analogy it seems to me the Protestant has placed their faith and trust that the ship has spotted them and will indeed rescue them. The Orthodox does not indicate this faith hoping that if they do something (e.g. swim out closer) they will be spotted and rescued. I think that is a fair analogy.