Something I commonly see is no standard for what means what, weapon wise. Some say the broadsword is a massive claymore, whilst others may think they're basket-hilted swords, and some even may think that they may just have a broad blade. I'm just going to make a quick list and what they'll be referred to here. Mind you, some of these are quite subjective, and will use the Chalcites as a standard.
Shortsword/Arming Sword - Any sword that, when held facing down from the hip, doesn't hit the ground, and only has room for one hand on the grip. Some shortswords, though, to be fair, are somewhat long.
Great Sword/Claymore - A large, two-handed sword. Occasionally has a space between the guard and a third or so of the blade which is not sharpened and covered in leather to assist with half-swording.
Longsword/Bastard Sword/Hand-and-a-Half Sword* - Any sword that has room for two hands, but is between the length of a claymore and an arming sword. When wielded with two hands, the second hand grips the pommel.
Broadsword - A shortsword with a basket-hilt. For a better idea of what they look like, I recommend you look up pictures of the Scottish basket-hilt broadsword.
*Just for clarification, a hand-and-a-half sword does not only have room for a single hand and a half. It has a full, two-handed hilt.
That's all I can think of right now. Will add more as they come to me. Currently only double-edged weapons, but I'll expand more.