First of all: consumer-grade S/PDIF can not carry more than 2 regular channels
Therefore it's necessary to compress audio.

The 2 de facto standards to squeeze sound are Dolby digital and DTS.
They were initially meant to be used in cinemas in an era where DVD wasn't even a thing, but what was previously high-end is now practically even in the worst of the receivers
Indeed movies almost always come with already encoded tracks that are usually straightforwardly passed-through (bitstream) to the amplifier, where they are decoded.
Though, the same is not true for games, that 99% (100%?) of times just output uncompressed LPCM audio

This is why Dolby Digital Live and DTS Interactive were created.
In short their task is to convert this raw bulky format to the aforementioned codecs.

Quality-wise they should actually sound similar, even though DTS is generally considered to sound louder (..or it's DD that sounds quieter)
Technically-wise Dolby Digital Live operates at 16-bit/48 kHz @640 kbps, while DTS Interactive rely on a 24-bit/48 kHz @1.5 Mbps stream.
Although the latter has more than 2 times the same bitrate, much of this advantage is lost in the not-so-useful 24 bits resolution and in the so-claimed-by-dolby less efficient compression.

Furthermore, both support additional tricks to "derive" up to 7.1 surround from stereo or 5.1 sources, with some of the channels "mixed" together to fit (aka matrixing)
They are respectively Dolby Pro Logic II(x) and DTS Neo:PC (take note that both had different revisions during the years)

Eventually... how to access these technologies?
A dedicated soundcard is definitively the best choice, though custom drivers for onboard chips and generic workarounds can also work.

This was the theory. Now let's see how things get messy.
^{trivia: did you know LFE channel is called .1 since it uses ⅒ of the bandwidth of the other channels?}

EDIT: DTS is possibly more error resistant than DD

Topic on Glossary talk:Sound