I think that we are both right actually... Doing a little more research shows that coax & optical digital can use either toslink or S/PDIF connectivity. The communications protocol is what determines the actual connection.
This is almost esoteric though as almost every digital optical output that I have seen uses the toslink standard and almost every coax output I have seen uses S/PDIF.
Definitions from Audioholics which match others I have seen on the net (I learned something new for sure, thanks!):
"SPDIF
SPDIF is an acronym for Sony Philips Digital Interface and is a CD “Red Book” standard digital audio transfer file format. A SPDIF interface can transport either stereo left-and-right channel information or multi-channel sound. It is typically found on audio and a/v equipment such as CD transports, Laser Disc players, DVD players, some digital satellite products and computer sound cards where it is implemented using an RCA connector. A SPDIF interface is a 75-ohm connection, identical to composite video in specification. Years ago many audiophiles felt that SPDIF offered better sound than the TOSLINK interface discussed below. Improvements in TOSLINK conductors have closed this performance gap and made concern over the interface a moot point.
TOSLINK
Short for Toshiba Link, TOSLINK is also a CD “Red Book” standard that allows for digital audio (both left and right channels or multi-channel sound) to be transported between components using an optical conductor and light as the carrier. Contrary to popular belief, TOSLINK does not use laser light but instead relies on the output of a simple LED. The Achilles heel of TOSLINK is the optical quality of the interface. The plastic conductors used in cheap cables can damage data and compromise performance.
TOSLINK connection performance is somewhat limited by the bend radius (bending a light conductor causes internal reflections and signal loss) of the conductor design. Additionally, the TOSLINK interface is length sensitive with maximum performance available only with runs of less than 20 feet."