You will notice that the medieval swords presented in the galleries all have a "type" either in title or at the beginning of description. It is not the century that is highlighted here but its classification in the so-called "Oakeshott" typology.
Ewart Oakeshott was a British collector of swords. His research has produced a classification of swords according to their blade, pommel and guard shape. Its typology is the most used and is the subject of research to improve it even today.
It's not the only grading method there is, and there are many others for different weapons.
Several specialists have studied the case of swords from the Middle Ages, but Mr Oakeshott has classified so many sources that his books have become the research axis for those who wish to find their way in the vast world of medieval swords.
You don't have to know the shapes of blades and pommels by heart to appreciate a sword, but your attraction to a particular type helps us to offer you other sources from the same family.
Here is what this typology looks like in its latest version:
As said before, other classifications exist.
Here is Petersen's concerning the handles of Scandinavian swords, from the 9th to the 12th century:
To go further we recommend the section "our sources", several books and links are available.