What's the difference between this and ordinary PTFE tape that has
been twizzled (technical term!) into a thread?

It's white synthetic fibre, not ptfe - I think. It's more like an
ultra-heavy-duty dental floss (more like the thickness of lacing cord
if you're familiar with that), with what feels like a waxy coating on
it. Let's call it dental floss for alligators.

I suspect because it's manufactured to be a cord, it has a reduced
tendency to chew up when being used on a rather rough or damaged
thread, and withstands quite a bit heavier mechanical loads. It's
certainly not a cord you can stretch or break between your fingers,
the box has a little dental-floss style cutter on it.

However the *practical* difference is that a damaged thread that I had
unsuccessfully tried to seal several times with tape (eventually going
as thick as I could - still without eliminating a very slight weep) -
sealed first time with this stuff.

And that or similar seems to be a common experience.

Considering the hassle of re-pressuring and still finding a slight
weep (which maybe you can cure, maybe you can't), I suspect many
people will spend a little more if they're likely to get a first time
perfect seal.