It's more about where the power comes from, and how brief the force application is.
Well, here's my take (and I think the above comment is very relevant):
As I posted earlier in this thread, there's big difference between a grinding lift and a ballistic lift. The ballistic lift requires tension over a brief time and then you get a float (which is basically the definition of ballistic -- you are launching a projectile). A DL is a grind. You have to sustain tension through a longer time and range of motion. The skills for both overlap (especially with similar hinge patterns like the swing and DL), but are not the same.
A big part of learning to deadlift well is learning to grind--generating high tension and then keeping it turned on long enough to complete the lift. As described in PTTP, your body has a fail-safe reflex that will try to shut the tension down. You have to learn to override this reflex to be disinhibited from expressing your strength. Lighter, more "explosive" swings by themselves don't do this. In fact, they train the opposite--to generate high momentary tension and then quickly shut it off in a rhythm of tight and loose--exactly what you don't want in a heavy DL.
My hypothesis is that heavier swings have a greater carryover to the DL than lighter swings done more "explosively" precisely because they "slower" (ESPECIALLY for a beginning deadlifter). I put "explosively" and "slower" in quotes because both terms conflate multiple parameters, the force/duration of the hip drive, the acceleration of the bell, and the period (total time) for the swing.
In a lighter swing, the force may be high, and the bell may have greater acceleration out of the hole, but the tension turns off quickly and you get a longer float. The bell goes higher, but that just extends the time of the period while the bell is decelerated by gravity. The period of a pendulum is determined by the height it swings to, independent of the weight. In a lighter, "faster" swing, more of the range of motion is passive pendulum motion.
With a heavier bell, the bell will have a lower acceleration, but the force is applied over a longer time. You can't just blast the bell out of the hole--you have to smoothly ramp up the power as the bell swings forward. The tension of the hip drive has to be sustained longer, through more of the range of motion, even if the height of the swing is less.
A lower height may also lead to a shorter period. You don't get as much float time, and have less opportunity to "rest while the dirt is in the air" (to quote S&S). So for an equivalent number of reps, with a heavier bell, you get more sustained time under tension and less relaxed "rest" time. Even if you aggressively "plank up" during the float of a lighter swing, the hip drive is over, and you are already in the lockout position at that point.
I'm not at all surprised that a beginning deadlifter with a strong swing would struggle with DLs once the weight gets a little challenging. The swing might establish a good hinge pattern and a baseline of strength, but does nothing to teach sustained tension and overriding the shut down reflex. I've seen Dan John recommend first learning the DL with a thick bar because you can't gun it off the floor; you have to ease it up smoothly ("ease" not meaning loose or relaxed, but in contrast to an abrupt yank).
For an experienced deadlifter, the calculus might be a little different, since the grinding skill is already established. Personally, I started training the DL after reading PTTP several years before I even knew what a KB was (Pavel had not yet come out with the original RKC book/video and you couldn't find a KB to buy in the US). I think that order of progression was actually beneficial and I'm glad it worked out that way.