I got a new TV and it has a SPDIF digital audio out...
You kind of answered your own question, your TV has Digital OUT. This usually means you have some form of a digital tuner, so the digital audio that is taken from the tuner can be output from your tv, to a receiver for a surround sound setup.
Simply put, you do need to have the receiver to be able to do anything useful!
Pic 1 is Digital Coaxial, while Pic 2 is Optical/Toslink, both are covered under S/PDIF (Sony/Philips Digital Interconnect Format)
With a cheap converter, one can be hooked to another, but you can not plug your PS3's SPDIF Output into your TV's SPDIF Output, they need to be plugged into a device with a SPDIF input, like an AV receiver.