It said nothing about the variety of swords (which is something Europe is
not alone in having)
European swords are extremly diverse critically in the Late Middle Ages - Early Modern Europe, probably more than Arabo-Islamic swords by exemple (and relativly better on quality for North Africa, even if it's not at all a given regarding Middle-East) at this time.
By exemple, in the XV-XVI, depending where you was, the most used sword could be a longsword, a semi-longsword, a rapeer, a sabre, a scimitar, a claymore, a spandona, a braquemard, an espada etc. t
It's not just names that are different, but use of the blade, size of the blade, against who, use mounted or dismounted or even both. Quickly, you have different codifiations as you have de facto two different weapons with their own distinctive cultural background.
On the other hand, Arabic swords were distinct from Morocco to Persia but used same bases from one edge to another, and if these distinctions are enough important to know where it comes from, their distinct evolution are not marked enough to call for a codification by variant.