The only correct use of the term "broadsword," IIRC, is for the Dao & for swords like the basket-hilt claymore & schiavona: "broadsword" is a term brought about after medieval times.
The term "long sword" didn't really exist in mediaval times, either: IRRC, I think that the term "long sword" was actually used for weapons more akin to a bastard sword. Medieval swords were just called "swords."
In essence, the "long sword" of 3E is more like the "normal sword" of Basic D&D: covers any 1-handed, straight-bladed sword which (typically) is double-edged, & typically uses the edge of the weapon to inflict damage rather than the point. The 3E longsword covers the old longsword & broadswords of 1st & 2nd Ed., & the "normal sword" of Basic D&D.
So basically, you have a set of stats that covers a bunch of weapons, from the Roman spatha, to the Viking sword, to the sword of medieval knights, and even the basket-hilt claymore or the schiavona; just like the scimitar can be used to cover such weapons as the cutlass, the saber, the tulwar, the hanger, the Chinese Broadsword or Dao, the Russian shashqa, & the storta.
On a side note, the only thing I didn't really see covered stat-wise is something to cover weapons like the falcata: to give you an idea, envision a short-sword sized weapon with a forward-curving blade like a kukri---that's a falcata. That could also cover similar weapons like the cruder khopesh, as well as the yataghan & other forward-curved weapons (a great example being the sword used by the Medjai in The Mummy & The Mummy Returns.