Ninja-To, Cutlass, Wakizashi: All just short swords, or something different?

Seeing the stats for a cutlass in Dragon #318, plus the ninja class proficiency list, reminded me of this:

Could a lot of weapons like the ninja-to, wakizashi, & ninja-to just be lumped under the "short sword" weapon category? Also, how big of a deal is it for a short sword to be classified as "slashing or piercing" instead of just "piercing" or "slashing" (or other types of swords, for that matter)?

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