You have daggers/knives, one-handed swords (aka arming or knightly sword), bastard-swords, and 'great' swords (which have a wide variety of names, including long sword). I agree that terms are pretty fungible though and I'm sure its arguable that many people called their 'bastard sword' a 'long sword', or simply referred to ALL larger swords as 'long'. I mean, your basically talking about a period of 1000 years or more just covered by Medieval Europe, and dozens of common languages, so...
The real point is, the idea of subdividing single-handed swords into different classes of weapon is questionable, at best. An 11th Century arming sword might have a slightly longer and thinner blade than a Legionary Hispanica of the 2nd Century, but they are generally very close in size and weight and would be used the same way (though the reasons for carrying them and who used them are radically different, as is their 'furniture').