It can be both or neither, they are not inclusive or exclusive terms. LSD transmission means it is equipped with a limited slip differential, the opposite of which is an open differential. You want the LSD, it forces power to both wheels, instead of an open diff which always sends it to the wheel with less traction.
Cable or Hydraulic refers to the mechanism that engages and disengages the clutch. Your CRX has a cable mechanism, a GS-R transmission uses a hydraulic mechanism that they probably developed for people who couldn't handle a hard clutch pedal. You guessed it, your car which is designed for a cable tranny is not compatible with a hydraulic transmission. You have to do some conversion work to make it happen with the GS-R trans.