Technically, I believe that D&D has gotten sword names messed up since the beginning and thus what people think of as a long sword is not really a long sword.
From what I understand historically, you have:
Swords - This term was used for anything from an arming sword, backsword, broadsword, sidesword, etc.
Long swords - IE a bigger sword, used 2 handed mostly.
Great Swords - even bigger Long Sword, the Montante is here.
Then came Rapiers, these are anything from the fencing blades we know of to the long and thin swept hilt blades mainly for thrusting.
Sideswords actually fit the shortsword category in D&D. Rapiers are LONG. A Sidesword is shorter. My group normally makes sideswords a shortsword that is variable either slashing or piercing damage.
