I came in near the end yesterday, but I think I've still got a handle on it.
For one thing, it's important to remember that the longsword and the arming sword aren't the same weapon.
Arming Sword: One handed, simple design, functional in all areas including the cut, the thrust and the parry. Served for a long time as a Cavalry weapon, and thus had comparatively little reach. The subject of over 9000 English epitaphs.
Long Sword: Two handed, superior thrusting device, could theoretically penetrate any kind of armor if half-handed or the enemy was rendered prone. The subject of over 9000 German fechtbooks.
Katana: Two handed (could be used one handed, this was only when used from horseback or by Musashi. Is actually short reached for a two handed sword, because it is abnormally thick, which is to increase its cutting power and durability. While katanas are actually not -too- fragile compared to other swords, their edges do chip in a dangerous fashion-they lose wedges instead of slivers. The subject of over 9000 animus.
Rapiers: A joint effort on the part of Italy, France and Spain to troll the shit out of the German dueling community. A very long sword, a very fast sword, a very deadly sword with a bit of accuracy, and very difficult to fight if you learned to fight real swords. Of dubious utility on the battlefeild due to its thin blade and lack of a good cutting edge, but many were hardy enough for it, and there were thicker swords of almost identical properties, like the sidesword. the subject of over 9000 pages of John Silver's bitching.
Cutlass: A short, chopping weapon designed for use on naval boarding actions, where close quarters and a lack of armor made cleaving cuts the coolest thing in school. Famously good on the defensive (almost certainly accidental, as the early ones didn't even have guards0 at least one Spanish manual recommended them as off-hand parrying weapons. The subject of over 9000 pirate deaths.