Swords, like any tool, are designed for particular purposes, and some designs are better at some things than others.

For example, katana are absolutely useless against plate armour, as they're designed for draw cuts, what with their long, curving blades. Conversely, rapiers aren't that great when you're on horseback, nor are they particularly useful as cutting weapons due to their relatively thin blades.

Another example would be falchions. They were, essentially, sword-axes that were great at hacking through limbs and mail, but once you run up against plate armour, a piercing blade with great point control - like a rapier - is more useful as you can find unarmoured points to strike your enemy.

Sabres and cutlasses were designed to slice and cut, with thrusting as a secondary consideration, which was a huge benefit in the ways they were intended as being used - as cavalry weapons, or as close combat weapons in tight quarters against unarmoured enemies.

Whilst /u/EyeStache has given a sufficient answer to your question, if you really wanted to dive deep into the "why", you'd have to analyse many centuries of military history and the development of not only armour and weapons but the entire strategies and fundamental concepts of war that drove different civilisations. This would be tied in to more than just that though - the way religion, politics, and philosophy affected these concepts of war are groups of many other factors that affected the different developmental lines between any two distinct civilisations.