The HK 55 is the corded version, HKC 55 is the cordless version.
Both work the same on the FSK rails, and work on the FS rails that the TS tracksaws and other systems run on.
The biggest difference I noticed in person between the two was that the motor on the HK 55 sticks out to the left past the rail edge, whereas the motor on the HKC 55 is flush with the edge of the rail.