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.
Yeah, scimitars seem pointless since they are literally the same as shortswords. Same damage time, same roll, same everything. The scimitar weighs 1 lb. more and costs 15 gp more than a shortsword. The blades are supposed to be longer, though. Maybe if they did something like greatswords do and roll multiple die, so it's a 2d3 weapon instead for more consistent damage, being more designed for slashing than normal swords. Game versions of scimitars usually have thicker blades than the real ones, and they look like the center part is weighted based on its thickness, which would let it swing even harder.
In real life, scimitars were THE weapon for horseback combat and were used for a long time. https://nationalinterest.org/blog/the-buzz/scimitar-how-one-sword-dominated-warfare-centuries-25033
I know that many things overlap in D&D as for weapon types, and it's mainly for appearance's sake, but there's not even a reach difference.