Well, the classification of weapons is fluid (at what exact lengh is the difference between short sword and long sword, and what do you measure to define lengh) and a computer game is not a simulation. In DnD every weapon has to fit in a weapon category and those categories have their stats for balance reasons, not for realism.
The category sabre does not exist in DnD, I think scimitar is the closest match.
So for the sake of simplicity and if we restrict ourselves to swords.
- rapier: long, straight and thin sword
- scimitar: any curved sword
- longsword: any sword that is neither very thin or very curved
- greatsword: any sword that is so large that you must use both hands in order to fight with it at all
- shortsword: anything that is smaller than the stuff above but taller than a dagger (sorry, I have no clear value for the lengh)
Rapiers deal 1d8 damage and they are finesse but NOT light (no dual wielding with it)
Scimitars and shortswords deal 1d6 damage and are finesse and light (dual wielding possible)
Once again, those rules have been made for balance, not for realism.
Most players and maybe also the creators of these rules are not experts for the classification of old weapons.
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