This is the least important thing that got brought up, so of course I kept thinking about it.
In 5.0, scimitars and short swords are identical except for their damage type (slashing versus piercing). Both are "light" weapons (which mostly means you can use them to engage in two-weapon fighting with) and "finesse" weapons (which means you can use either strength or dexterity with them).

In the stock rules, monks get special access to short swords, but not scimitars:
At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
There's an optional rule in Tasha's that gives monks more stuff, but I'll never use it. You picked monk, use monk weapons. I might feel different if I didn't have gems to stick on your weapon, because it's not like any loot table is gonna hand out +3 nunchucks.

Rogues don't get special weapon lists, but they do have limited proficiencies:
"Simple weapons, hand crossbows, longswords, rapiers, shortswords"

Did a scimitar of speed show up? Your rogue really wants that*, but he can't use it unless he:
1- Multiclasses to some class that offers martial weapon access, like Fighter, Paladin, Barbarian, or Ranger
2- Get the Weapon Master feat**
3- Have a race that gets access to some non-scimitar weapon and bully your DM into allowing the Tasha's optional rule that only weenies use, that lets you change a race's thematic weapons to whatever is most optimal for you
4- Just be an Elardrin and know it ok, they just can know it and I think Astral Elves can too or something maybe elves just vibe with things ok

Anyway, if you actually have martial weapon proficiency and aren't restricted, you use a scimitar or a shortsword mostly interchangeably.

In 5.5 this is different because scimitars and shortswords have different weapon masteries. I'm not sold on the weapon masteries for my games, which are never gonna be 5.5 baseline (I'm willing to take in certain elements obviously). I wouldn't mind expanding the weapon design at some point, especially if the Kenda Gems work as well as I hope. Right now if you want to be a Drizzt clone or whatever in a game with drow and rangers and scimitars, man, it doesn't work good. Even in 5.5 you never want two of them, a scimitar user only ever wants one.

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*The scimitar of speed lets you make one attack with it a bonus action on each of your turns. Unlike two weapon fighting, this doesn't require you to wield a second weapon OR to have spent your attack action, so you can just open your turn with it, and, if it hits, then use your action to ready an attack for after your turn (this costs your action and your reaction). This lets you get an attack on your turn and one off your turn pretty reliably. I'll never hand out a scimitar of speed, though there could be a Kenda Gem that offers such a power, likely only for light weapons.

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**The stock Weapon Master feat gives you:

Weapon Master
+Increase your Strength or Dexterity score by 1, to a maximum of 20.
+You gain proficiency with four weapons of your choice. Each one must be a simple or a martial weapon.

This feat is terrible. Instead I offer (Feats and Languages v1.3, p11):
Martial Initiate
You have practiced extensively with the arms of war, gaining the following benefits:
+Increase your Strength or Dexterity score by 1, to a maximum of 20.
+You gain proficiency with light armor, simple weapons, and martial weapons.