Well, they both do the same thing, and do it equally well, but they are not the same cable.
Digital coax is just a high quality RCA cable. SPDIF, also called TOSLINK or Optical Digital Audio, uses a special cable made of a single strand of optics quality plastic to carry the audio signal as a beam of light.
Both are cables used to carry a surround sound signal although I've never heard of a converter for going from one to the other.
If your receiver has an input for digital coax, it should have at least one optical audio input as well.
The other issue, your TV may only send an audio signal from the optical audio port for certain types of inputs. For instance, my TV only does this if I'm using an antenna. It will not work for the other AV inputs. You'll have to check your TV's manual to find out. You may also need to turn off the TV's speakers in order to get anything to use the audio outputs on the TV at all.
Finally, remember that almost everything broadcast on TV/cable/satellite is only in stereo sound. So even if you get this working, for almost all programs, only your LG's front speakers and subwoofer will actually be emitting sound.