Are rapiers and scimitars considered swords for magic items like:
Or are only shortswords (not Sword of Sharpness or Vorpal Sword), longswords and greatswords swords for these items and therefore available?
5e does not specify specific weapon categories beyond the name of the weapon. One could say that each different name is a different weapon type, but that would mean that shortswords were a different weapon type than longswords or greatswords.
Because of this, I believe it makes much mores sense to consider that by the type "sword" for these magical items they mean any type of sword using the real world definitions for what a "sword" is, making both scimitars and Rapiers fall under that definition and therefore count as the "sword" type when dealing with magical items.
The best I could find in the books is that the Frost brand (171, DMG) Art depicts the sword as a scimitar (the Frost brand is a magic weapon that can be any sword). And the description of the bladesinger cat style:
Cat. Styles that employ a sword belong to this family. (...) Red tiger, a style just three centuries old, has its bladesingers using the scimitar in a whirling dance of defense (142, Sword of the coast adventure's guide)
unfortunately they look more like fluff. And I couldn't find anything specific about the rapier.
But maybe we can use some history to classify the rapier as a sword. The word rapier, according to wikipedia:
The word "rapier" is a German word to describe what was considered to be a foreign weapon
The rapier first name was the spanish word "Espada ropera" or "dress sword". The people of that time also called the dress sword just "Espada" (Which translates to "Sword").
Sources:
A sword consists of a long blade attached to a hilt. The blade can be straight or curved (...) The thrusting swords such as the rapier (...) (Wikipedia: Sword, Emphasis mine)
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Non-European weapons called "sword" include single-edged weapons such as the Middle Eastern scimitar (...) (Wikipedia: Sword, Emphasis mine)
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Rapier or Espada Ropera, is a loose term for a type of slender, sharply pointed sword (...) The word rapier was not used by Italian, Spanish, and French masters during the apogee of this weapon, the terms spada, espada, and épée (or espée) being instead the norm (generic words for "sword") (...) (Wikipedia: Rapier, Emphasis mine)
It depends: Who do you want to get the item?
If you want the item restricted to the martial classes, bards, and rogues, then "sword" means "longsword".
If you include "scimitar" then the item can also be used by druids.
Rogues still might not want a magical longsword - they want finesse weapons. So, if you include "rapier" then every Rogue is going to want the magic item.
Historically in D&D, more magical weapons were longswords because fighters were the only ones who could use them. Having more magical longswords than other weapons helped balance the "linear warrior - quadratic wizard" problem.
As an aside, if you want to restrict the magic weapon to the martial classes only then make the item a greatsword or glaive (which is just a sword with a really long handle) or maybe a battleaxe (for example, Snaga, the axe of Druss the Legend).
