SPDIF cable same as coaxial cable?

To answer your question, S/PDIF is a specific digital communication protocol to encode and transfer 2-channel PCM music data as well as multi-channel Dolby Digital and DTS data.  Technically speaking, any wire can be used to connect an S/PDIF source to a S/PDIF target/receiver.  However, COAX cables are mostly recommended because of their shielding (which is critical on a S/PDIF cable) and the ability to try to adhere to the 75 ohm requirement for S/PDIF transmitter/receiver specification.  In reality, only COAX cables properly terminated with a 75 ohm BNC connector will match this criteria.  Cables that are terminated with RCA generally have a lower impedance (I think it was somewhere around 24 ohms or so).

There are a couple of other mechanisms that have been created to transfer this same S/PDIF data:

toslink - a glass/fiber cable which uses light pulses to transmit the S/PDIF data instead of electrical pulses.  Like others have said, it electrically disconnects the source/target so that there is no ground loop hum transmitted.  The downside is that it's not a perfect transfer medium because the LEDs (light emitting diodes) just cannot light up fast enough to create a perfect square wave.  The result is almost a curvy sine wave.  Sound quality is not going to be as good as a high quality COAX.

AES/EBU - uses an XLR cable that should be engineered to have 110 ohm impedance.  The digital pulses are exactly the same as digital COAX, except they are balanced.  One conductor of the XLR transmits a positive square wave, and the other conductor transmits a negative square wave.  Generally, both of these conductors are connected to the primary wires of a small transformer on the target/receiver (one conductor pushes voltage while the other conductor pulls voltage).  Theoretically speaking, you could take the positive conductor and just connect it into a standard digital COAX input (because the signal is exactly the same).

The above is a very thoughtful and informative answer.

Is a coaxial cable same as a SPDIF cable?  Seems they are one in the same.

The simple answer in home audio applications is yes.

Coax with a BNC termination will conform to the 75ohm S/PDIF standard.
I have been told by a cable designer (Rick Schultz) that RCA digital coax can come close to 75ohms depending on the design.

http://www.bluejeanscable.com/articles/75ohmrca.htm

auxinput,
great job!

AES/EBU - uses an XLR cable that should be engineered to have 110 ohm impedance.

Like with S/Pdif, AES/EBU is an audio transfer standard and not the cable.  It can be used with 110 ohm XLR cable (IEC 60958 type I), with 75ohm coax or Toslink (IEC 60958 type II).    XLR is just most common cable with AES/EBU.

The main difference between S/Pdif and AES/EBU standards is in the property rights.  S/Pdif includes Serial Copy Management System, preventing second-generation copy in some instances.  Most of AES/EBU used in consumer audio is S/Pdif standard.  It is assumed to be 110 ohm XLR only because that was the most common use of AES/EBU (studios).

Also, AES/EBU was defined as 24 bits while S/Pdif was 20 bits + 4 auxuliary bits, but these 4 bits are used (almost always) as data extension to make total of 24 bits.

So, in consumer audio both "AES/EBU" and "S/Pdif" follow S/Pdif standard and name difference is customary for different cables and electrical levels.

If the AES3 XLR cable can be connected to RCA with a simple adapter it is SPDIF which is really now considered a variant of AES3 if you need an impedance converter for it to work it is AES3 type 1 or the old AES/EBU standard. AES3  is used in professional installations with XLR 110 Ohm balanced or BNC 75 Ohm unbalanced.