Road bike saddles tend to have less padding and are focused mainly on saving weight. They vary in widths and care meant to fit to your hip bones. Most road bike saddles allow for a more aggressive position on the bike and provide a more aerodynamic position for the rider.
Sport saddles are designed to fit well with hybrid bikes. Usually they have more padding than a road bike saddle, but not quite as much as a full-on comfort saddle. For the rider trying to ride a long ride and finds road saddles uncomfortable, a slightly more padded sport saddle would be the right choice.
Comfort saddles are for the rider looking simply for comfort and nothing further. These saddles tend to have lots of gel or foam padding, and usually weigh more than road or sport saddles. Comfort saddles have the most cushion and are for riders looking for an all-around comfortable ride.