The catadioptric is a bit of a “recoil TIR” actually.
First the light bounces off the front surface on to the alu plated (presumably parabolic) reflector and then through the front in (hopefully) parallel rays.
A neat principle i.m.o.
I’ll get one, one day.
But what could be so special about that Seoul P4?
Does it sit deeper in the optic?