The Japanese measure blade length by foot.
The length of D&D blades correspond as follows.
• 0+ feet: dagger
• 1+ foot: shortsword
• 2+ feet: ?
• 3+ feet: longsword
• 4+ feet: greatsword
The sword that is missing in D&D is actually the important one: viking sword, knightly sword, spatha, katana, etcetera.
Some of the 3+ ft weapons might be covered by the scimitar, or shortswords pushing into rapier category, but most would be 5e longswords. The shorter ones are less optimised towards two-handed capability; as the length of the weapon pushes towards 4ftish, designs generally become more optimised for two-handed use.
There is no definite demarcation point however, and you have outliers like the katana, which has a short, heavy blade like a falchion but an extended handle for two-handed use, or the arming sword where the two-handed techniques involve gripping the blade, rather than the pommel.
If there are any historical swordfighters among us, what is the main difference in feel between a single-edged sword and a double-edged sword?
I'd personally say that the actual design of the sword matters, and styles of use vary considerably rather than being able to give a straight answer comparing 'single-edged' vs 'double edged'. The katana and falchion/messer feel similar in the hand for example, but actual design and styles of use are very different.
If you took a longsword for example, and ground off one edge, the feel and overall style wouldn't change much, although obviously you wouldn't be using 'false edge' techniques.
Likewise, the sabre, katana and some of the Indian tulwars/scimitars have very similar blades. (Often literally the same blades; the British in India had a lot of praise for the Indian warriors and often refitted tulwars into sabres and vice versa. Likewise the Portuguese in Japan did a roaring trade in sabre blades to be refitted as katana.)
Looking at the different styles in use however, the weapons seem very different.