When most Americans think of swordplay, the images that come to mind are either of the lumbering power of armor-clad knights battling with broadswords, or of the swashbuckling flair of Errol Flynn and other screen duelers of the '30s and '40s. In what it requires and how it is conducted, Olympic fencing resembles these two clichés about as much as the Olympic Opening Ceremonies resemble the ritual sacrifice of animals that once signalled the start of competition.
If the "real thing" is a duel with sharps, then aside from the mortal danger and related psychological factors, the primary technical difference is that the duelist can win with only a single good touch, whereas the athlete has to hit his opponent as many as 15 times and so requires more technical and tactical depth. Many inferior duelists have won their combats through sheer dumb luck. This is far less likely in the sport. On the other hand, the sport fencer takes many defensive risks that would be unthinkable in a duel, since he has up to 15 "lives" to work with. Some purists equate "real" fencing with classical fencing, ie. the prevalent styles of the traditional French and Italian schools of fencing that predominated before electric fencing was popularized. By comparison, modern fencing is more mobile and athletic, while classical fencers were known for their more sophisticated phrasing and bladework.
When a fencer climbs the podium to receive their medal, they are not just representing themselves. They're representing the team of people who worked together to get them there.