The term 'long sword' was used to refer to a two-handed sword, universally. Actually one-handed swords were almost entirely personal defense weapons designed for easy carrying as a supplementary weapon, or when NOT otherwise 'armed' (hence their name, 'arming sword'). There was really not much in the way of purely one-handed blades longer than about 30", which ARGUABLY could be classified as 'short swords' by D&D's parlance (another term that is ahistorical, but at least it was not used for something else at any time in history). I mean, Roman 'hispanica' and similar were in this range, and apparently D&D's short sword is meant to model them.
So, names like dagger, arming sword, bastard sword, and long sword would be pretty accurate historical labels that would cover the range of actual sword-weapons pretty effectively. In the earlier periods, or as military issued weapons, you see something in the 'arming sword' range pretty often, combined with a shield, but even then such warriors almost universally carry spears, javelin-like dart weapons, and often some form of axe, as either a primary or backup to the sword. Later, when heavier armor comes into fashion most of your professional warriors (IE like knights) often dropped the shield and if they wielded a sword in battle it would be two-handed (a true long sword).
Mostly the division of one-handed swords into 2 separate length/weight categories is not justified, and the nomenclature used by D&D is way off.