At first glance, the differences between sabers and rapiers appear obvious. Although both are one-handed swords, the shape of the blade and how it is used are vastly different. Let's take a closer look at these fascinating blades.
Rapiers are straight, thrust-oriented swords. Although it is not common, there are historical examples of the top third of the blade being sharpened and honed to a fine edge so that the blade can double as a draw cut specialist increasing the usefulness of this type of blade. They are double-edged generally, and often have some form of basket hilt of bent bars, stamped metal, D guard or other full hand protection offering an extra level of safety for the hand. With a reputation for being both elegant and deadly, rapiers came to prominence in the early European Renaissance and were made famous with movies and books like the Three Musketeers and Robin Hood. While the rapier sword made an excellent thrusting weapon, it was also adept at cutting and many martial art styles focused on inflicting several cut wounds on an opponent causing them to fatigue or perish from loss of blood. While thicker and longer versions dubbed "battle rapiers" existed for use in prolonged combat, the rapier saw the most popularity as a civilian blade. A status symbol for nobility and the weapon of choice for settling heated disputes. There were so many duels fought in France a law needed to be passed outlawing the practice. Too many good fighters were dying and getting hurt which is not a good thing when soldiers are needed while contemplating war with England. In this way, the rapier preceded what would come to be known as the "court sword" which is a sign of nobility and honor.
As for the saber, this sword was usually curved and is more of a cut-oriented blade. Single-edged but frequently has the back edge of the blade near the tip sharpened to make piercing easier. Some hand protection ranging from a metal bar to a more complete shell guard can be found in examples of this sword. Sabers and their curved shape evolved from Eastern blades where the style was prominent. Although the sword was adopted by civilians in some cases, the saber largely remained a military weapon. The most beloved swords in military history were the sabers of Napoleon, Wellington, Robert E. Lee, Grant, and others. So efficient was this shape at cutting bone, flesh and even chain mail that the east adopted it early in history as the preferred battle sword of its day. Genghis Khan, the prophet Mohammed and many emirs treasured such blades for court use, directing the military and for cutting down foes. They could be used extremely well in trained hands from horseback making them a decisive weapon before projectile weapons took over the battlefield.
To conclude a saber evolved from Eastern origins and favored heavy cuts and slashes, while the European styled rapier used it's finesse to effectively thrust and slice at opponents. While neither of these swords was restricted to these types of cuts, a clear preference can be seen.