This is a categorization that developed as I was learning FMA material and thinking about how hard it would be to use a lot of the material in fencing. When evaluating a blade, people tend to think of length, balance, weight, etc, in terms of attacking. From that respect, there aren't any clear lines in length. However, I realized that, defensively, there are some clear boundaries.
Knife length is where stopping the hand is enough to save you. Imagine someone thrusting at your heart and you catch their hands with both of yours, arms bent just under 90 degrees to the muscle power zone. That distance from hands to chest is where I would draw the line categorizing a knife. This is also about the length from shoulder to elbow- the distance you get from tapping with your forearm. As these are defensive, body-based categories, they're going to be different from person to person, but generally it's about 12-14 in. Those that would class for knives as very tall individuals, but not shorter ones, could be called long knives.
Another key feature is that, to stop an attack by a longer blade, you (generally) must block, not parry or deflect. The blade is not long enough to provide a counterweight leverage advantage or to deflect a blade all the way off the body. Once you do block, there is a problem with framing. With longer blades, when you block with the bottom third of the blade, there is a clear disincentive in trying to go around the tip. With a knife, it is about equidistant for the attacker to go around the tip or around the hand, presenting the defender with a clear problem in constructing tactical trees. (Future research: Is there a blade length at which it is always possible to cutover before the defenders reacts?)
(also: geometry, angles, interception and length)
2. Short sword
A knife becomes a short sword at the length where, if you caught the hand, it would not prevent the weapon from stabbing or cutting. However, once an attack was evaded or blocked, the defender would be able to get a hand on the attacker the attacker to aid in further evasion/control. At this length, deflection becomes possible, as the short sword can form a wing over at least half the body, although it is not enough to prevent retracking once it is past the tip. Parrying is more possible, although somewhat tricky as angles great enough to provide force dissipation also open up the framing problem again.
This was the biggest disconnect for when I was learning the FMA stuff. The knife stuff all made sense, and the short sword stuff made sense in doing it, but I felt like it would be problematic against fencing technique (at least in terms of first blood. It was totally clear that, while I felt confident I could get first blood against most FMA practitioners, nothing in my fencing training would stop them from killing me after that). So, sword length: after stopping an attack, you still cannot reach the opponent's hand. (footwork aside) This seems like it would be just another reach issue, but has more ramifications than that. For instances, deflections with short swords work because as the attacking blade nears the tip of the defending blade and begins to collapse it, the defender can check or pass the opponents hand to prevent tracking. This is problematic against a sword, unless working espada y daga. Also, the length of a sword makes parrying and retaining control of an opponent's blade far easier and more reliable.