Captain James Ross was the first of the modern explorers of Antarctica. He described a number of features visible from his ship, including what was later called the Ross Ice Shelf.
Scott was the first to explore Antarctica scientifically: the Discovery Expedition (1901) included geologists, meteorologists, and biologists. This expedition made no attempt to reach the South Pole.
Roald Amundsen went south in 1910 specifically to reach the Pole. With four other men he reached the Pole in December 1911, leading the first expedition to reach that point. He returned to his ship uneventfully.
In 1910 Scott returned to Antarctica in charge of the Terra Nova expedition. It was not until he reached Australia that he learned of the Amundsen expedition (Amundsen was supposed to be going to the Arctic, but changed his mind). He was poorly prepared and poorly organized for the journey; he arrived rather late in the Antarctic summer. He arrived at the Pole and found a note from Amundsen, who had arrived five weeks earlier. On the return trek his team was trapped by storms, ran out of food, and the three men died from hunger, cold, and exhaustion. I believe the tent in which they died still stands.
Shackleton accompanied Scott on the Discovery Expedition but fell ill and had to return home. He returned to Antarctica in 1914 with the intention of trekking to the Pole and, rather than returning, continuing on so as to cross the whole continent. His ship, the Endurance, became trapped in the expanding sea-ice, and after riding out the severe Antarctic winter, was eventually crushed. Shackleton salvaged what he could and led his men, carrying their gear and two lifeboats, on a long trek to the coast. He left most of his crew in camp and sailed, with five others, in a lifeboat to the nearest place where there would be a ship to rescue them. In the end he brought all his men home.
So: Amundsen reached the Pole and returned safely; Scott got to the Pole but died on the return; Shackleton barely got ashore but survived the winter, the loss of his ship, a long trek in retreat, a longer voyage in an open boat, and returned safely.
Why the difference? How did each of the leaders bring about the manner of each expedition's ending?
Amundsen had a great deal of experience in both the Arctic and Antarctic. He learned from the Eskimos how to survive in the North: proper food, clothing, and equipment that would keep his people alive. This knowledge, his own common sense, and some luck with the weather, helped his own expedition make a businesslike trip to the Pole and back.
Scott was very different. Discussions of his failure continue to this day. It seems he had neither the practical experience of Amundsen, nor his common sense, his ability to lead an expedition to success, or his luck. He seems to have relied more on the British idea of "muddling through" than on planning, preparation, and training.
Shackleton's trip was aborted at the very beginning, through no fault of his own. Once he had to abandon the idea of proceeding, he showed extraordinary ability to keep his people alive, healthy, and confident. When it was time to retreat, he showed equal ability to lead the men on a very difficult journey without losing any of them. I think this is perhaps the greatest example of leadership I have ever heard of.