They are the same thing, sort of...
Lightpipe, optical, and TOSlink each describes the cable. It is basically a piece of plastic or flexible glass that can carry a beam of light to the other end.
ADAT describes the type of signal that goes through the cable. It is a single beam of light that blinks on and off real fast to create a sort of digital code. Both the sending unit and the receiving unit must be ADAT format. ADAT can deliver 8 separate channels simultaneously through one cable. (I am guessing 6 of these cables will enable you to send 24 channels and to receive 24 channels.)
Optical cables can be used for other digital formats (languages) as well, such as s/pdif which usually delivers 2 channels.
The cable should not be bent, cracked, or broken. The ends should be protected from scratches and kept free of dust.
Hope this helps.
