What is the difference between "surely" and "definitely" in this context?

"Surely" can mean "with full success". However, "definitely" tends to mean "without a doubt".

EDIT: I hadn't seen that the words were made links. To further elaborate on my answer, I am going to try to stay within your given example's particular context:

By saying the dolphins were definitely attempting to help them, you are saying that there was no doubt whatsoever that the dolphins were there to help. Surely could perhaps gives off the same meaning. However, when I put it in the place of definitely, I tend to believe that the message is trying to be conveyed as they were successful in their attempt to help the life guards. I could be overreaching here, but think of it this way: If you replace surely with the word "successfully"-- which might sound weird-- you get a different meaning. Essentially, by using definitely, you are preventing the ambiguity that arises with other meanings of surely.