Swords are straight or curved weapons consisting of a bladed edge or often double edges. it can be used for cutting, slashing, thrusting, slicing, stabbing, jabbing, and piercing. It can also be one-handed or two-handed depending on design and preference.
Shortswords are smaller variants of the one-handed longsword. Though generally weaker than it's longer counterpart, it is perfect for those who utilize speed and flexibility while maintinaing an overall effectiveness in blade-to-blade combat. For a list of notable users, see here.
Longswords are the standard one-handed sword. It is generally the heaviest, most damaging variant of one-handed swords. Unlike it's shorter counterpart, longswords are better at parrying and redirecting some melee attacks. At the hands of a skilled user, longswords can even be used to deflect some projectiles with proper and highly-disciplined training.
Claymores, also referred to as greatswords, were the heaviest variant of swords. It's long-reach, weight and design were favored by barbarian-style fighters who preferred weapons with great cutting power while maintaining good range. It can also be used for thrusting and slashing. With the proper technique and skill, a greatsword user can easily sunder their opponent's shield or weapon, and even their armor, often yielding fatal results against the victim.