From Wikipedia:
AC'97:
AC'97 (short for Audio Codec '97; also MC'97, short for Modem Codec
'97) is Intel Corporation's Audio Codec standard developed by the
Intel Architecture Labs in 1997, and used mainly in motherboards,
modems, and sound cards.
Audio components integrated into chipsets
consist of two components: an AC'97 digital controller (DC97), which
is built into the I/O Controller Hub (ICH) of the chipset, and an
AC'97 audio and modem codecs, which is the analog component of the
architecture. AC'97 defines a high-quality, 16- or 20-bit audio
architecture with surround sound support for the PC. AC'97 supports a
96 kHz sampling rate at 20-bit stereo resolution and a 48 kHz sampling
rate at 20-bit stereo resolution for multichannel recording and
playback.
HD Audio:
Intel High Definition Audio (also called HD Audio or Azalia) refers to
the specification released by Intel in 2004 for delivering
high-definition audio that is capable of playing back more channels at
higher quality than previous integrated audio codecs like AC'97.
During development it had the codename Azalia.
Hardware based on
Intel HD Audio specifications is capable of delivering 192-kHz 32-bit
quality for two channels, and 96-kHz 32-bit for up to eight channels.
However, as of 2008, most audio hardware manufacturers do not
implement the full high-end specification, especially 32-bit sampling
resolution.
The reason the MC'97 is tied to the AC'97 is to provide interaction between the MC'97 modem and the AC'97 speakers/mic, for using it like a "voice modem".