Transwarp transporter must be a completely new type, as the regular type never does FTL or long distances.
Actually it's a very OLD concept that nobody could ever get to work properly. The first experiments with transwarp beaming took place in the 22nd century not long after the development of Starfleet's earliest transporter systems; Trip even mentions to Archer that the modifications to the transporter were mainly just superficial and despite the increased capability of their transporter system, didn't seem necessary for transwarp beaming anyway.
So it is not and has never been all that different from standard transporter technology. The only real difference seems to be figuring out a way to guide the carrier wave to its destination, and that turns out to depend on that one crucial equation.
I kind of thing it's a bit like somebody having rocket technology without having ever discovered calculus or the Tsilkovsky Rocket Equation. You could get rockets to fly short distances -- say, Germany to London and vice versa -- but planning interplanetary trips would be profoundly difficult since you cannot accurately account for either your ship's delta-v budget. At least, not until the older version of Jim Lovell writes something down on your notebook and you think "Shit, it never occurred to me to think of propellant
as part of the payload!"