You might have missed the line in Balanced Blade's description that it's 'A small sidearm to a longer, heavier weapon, perhaps.' The Old Country is
largely based on the Heian Period, so if you want to look at weapons from that time the Swift Sword would be more of a tachi than a katana and the Balanced Blade would probably be a tanto, maybe a kodachi if you want to play a bit loose with the timing because this is a game and not a work of historical fiction.
On that note, Tobs has mentioned that
Not!Japan kind of sped through a bunch of periods so it's not going to be strictly limited to any one in particular even if the bulk of influence comes from Heian Japan. So yeah, depending on what period you want to imagine the weapons are from, Balanced Blade would be a tanto, kodachi or wakizashi and the Swift Sword would be a tachi, katana or
maybe an odachi, though those aren't really meant to be used one-handed.
This concludes Wolfram's Weeb Hour, back to your regular programming.